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2*cos^2(x)+sqrt(3)*sin(x)=0 la ecuación

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Solución numérica:

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Solución

Ha introducido [src] 
     2        ___           
2*cos (x) + \/ 3 *sin(x) = 0
3sin⁡(x)+2cos⁡2(x)=0\sqrt{3} \sin{\left(x \right)} + 2 \cos^{2}{\left(x \right)} = 0
Simplificar
Solución detallada
Tenemos la ecuación
3sin⁡(x)+2cos⁡2(x)=0\sqrt{3} \sin{\left(x \right)} + 2 \cos^{2}{\left(x \right)} = 0
cambiamos
3sin⁡(x)+cos⁡(2x)+1=0\sqrt{3} \sin{\left(x \right)} + \cos{\left(2 x \right)} + 1 = 0
−2sin⁡2(x)+3sin⁡(x)+2=0- 2 \sin^{2}{\left(x \right)} + \sqrt{3} \sin{\left(x \right)} + 2 = 0
Sustituimos
w=sin⁡(x)w = \sin{\left(x \right)}
Es la ecuación de la forma
a*w^2 + b*w + c = 0

La ecuación cuadrática puede ser resuelta
con la ayuda del discriminante.
Las raíces de la ecuación cuadrática:
w1=D−b2aw_{1} = \frac{\sqrt{D} - b}{2 a}
w2=−D−b2aw_{2} = \frac{- \sqrt{D} - b}{2 a}
donde D = b^2 - 4*a*c es el discriminante.
Como
a=−2a = -2
b=3b = \sqrt{3}
c=2c = 2
, entonces
D = b^2 - 4 * a * c = 

(sqrt(3))^2 - 4 * (-2) * (2) = 19

Como D > 0 la ecuación tiene dos raíces.
w1 = (-b + sqrt(D)) / (2*a)

w2 = (-b - sqrt(D)) / (2*a)

o
w1=−194+34w_{1} = - \frac{\sqrt{19}}{4} + \frac{\sqrt{3}}{4}
w2=34+194w_{2} = \frac{\sqrt{3}}{4} + \frac{\sqrt{19}}{4}
hacemos cambio inverso
sin⁡(x)=w\sin{\left(x \right)} = w
Tenemos la ecuación
sin⁡(x)=w\sin{\left(x \right)} = w
es la ecuación trigonométrica más simple
Esta ecuación se reorganiza en
x=2πn+asin⁡(w)x = 2 \pi n + \operatorname{asin}{\left(w \right)}
x=2πn−asin⁡(w)+πx = 2 \pi n - \operatorname{asin}{\left(w \right)} + \pi
O
x=2πn+asin⁡(w)x = 2 \pi n + \operatorname{asin}{\left(w \right)}
x=2πn−asin⁡(w)+πx = 2 \pi n - \operatorname{asin}{\left(w \right)} + \pi
, donde n es cualquier número entero
sustituimos w:
x1=2πn+asin⁡(w1)x_{1} = 2 \pi n + \operatorname{asin}{\left(w_{1} \right)}
x1=2πn+asin⁡(−194+34)x_{1} = 2 \pi n + \operatorname{asin}{\left(- \frac{\sqrt{19}}{4} + \frac{\sqrt{3}}{4} \right)}
x1=2πn−asin⁡(−34+194)x_{1} = 2 \pi n - \operatorname{asin}{\left(- \frac{\sqrt{3}}{4} + \frac{\sqrt{19}}{4} \right)}
x2=2πn+asin⁡(w2)x_{2} = 2 \pi n + \operatorname{asin}{\left(w_{2} \right)}
x2=2πn+asin⁡(34+194)x_{2} = 2 \pi n + \operatorname{asin}{\left(\frac{\sqrt{3}}{4} + \frac{\sqrt{19}}{4} \right)}
x2=2πn+asin⁡(34+194)x_{2} = 2 \pi n + \operatorname{asin}{\left(\frac{\sqrt{3}}{4} + \frac{\sqrt{19}}{4} \right)}
x3=2πn−asin⁡(w1)+πx_{3} = 2 \pi n - \operatorname{asin}{\left(w_{1} \right)} + \pi
x3=2πn−asin⁡(−194+34)+πx_{3} = 2 \pi n - \operatorname{asin}{\left(- \frac{\sqrt{19}}{4} + \frac{\sqrt{3}}{4} \right)} + \pi
x3=2πn+asin⁡(−34+194)+πx_{3} = 2 \pi n + \operatorname{asin}{\left(- \frac{\sqrt{3}}{4} + \frac{\sqrt{19}}{4} \right)} + \pi
x4=2πn−asin⁡(w2)+πx_{4} = 2 \pi n - \operatorname{asin}{\left(w_{2} \right)} + \pi
x4=2πn+π−asin⁡(34+194)x_{4} = 2 \pi n + \pi - \operatorname{asin}{\left(\frac{\sqrt{3}}{4} + \frac{\sqrt{19}}{4} \right)}
x4=2πn+π−asin⁡(34+194)x_{4} = 2 \pi n + \pi - \operatorname{asin}{\left(\frac{\sqrt{3}}{4} + \frac{\sqrt{19}}{4} \right)}
Gráfica
0-80-60-40-2020406080-1001005-5
Trazar el gráfico f1(x)
Trazar el gráfico f2(x)
Suma y producto de raíces [src] 
suma
      /    /                            ____________\\         /    /                            ____________\\       /    /                            ____________\\         /    /                            ____________\\         /                          ____________\         /                          ____________\
      |    |    ____     ___     ___   /       ____ ||         |    |    ____     ___     ___   /       ____ ||       |    |    ___     ____     ___   /       ____ ||         |    |    ___     ____     ___   /       ____ ||         |  ___     ____     ___   /       ____ |         |  ___     ____     ___   /       ____ |
      |    |  \/ 19    \/ 3    \/ 2 *\/  3 - \/ 57  ||         |    |  \/ 19    \/ 3    \/ 2 *\/  3 - \/ 57  ||       |    |  \/ 3    \/ 19    \/ 2 *\/  3 - \/ 57  ||         |    |  \/ 3    \/ 19    \/ 2 *\/  3 - \/ 57  ||         |\/ 3    \/ 19    \/ 2 *\/  3 + \/ 57  |         |\/ 3    \/ 19    \/ 2 *\/  3 + \/ 57  |
- 2*re|atan|- ------ + ----- + ---------------------|| - 2*I*im|atan|- ------ + ----- + ---------------------|| + 2*re|atan|- ----- + ------ + ---------------------|| + 2*I*im|atan|- ----- + ------ + ---------------------|| - 2*atan|----- + ------ + ---------------------| - 2*atan|----- + ------ - ---------------------|
      \    \    4        4               4          //         \    \    4        4               4          //       \    \    4       4                4          //         \    \    4       4                4          //         \  4       4                4          /         \  4       4                4          /
−2atan⁡(−23+574+34+194)+(−2atan⁡(34+194+23+574)+((−2re⁡(atan⁡(−194+34+23−574))−2iim⁡(atan⁡(−194+34+23−574)))+(2re⁡(atan⁡(−34+194+23−574))+2iim⁡(atan⁡(−34+194+23−574)))))- 2 \operatorname{atan}{\left(- \frac{\sqrt{2} \sqrt{3 + \sqrt{57}}}{4} + \frac{\sqrt{3}}{4} + \frac{\sqrt{19}}{4} \right)} + \left(- 2 \operatorname{atan}{\left(\frac{\sqrt{3}}{4} + \frac{\sqrt{19}}{4} + \frac{\sqrt{2} \sqrt{3 + \sqrt{57}}}{4} \right)} + \left(\left(- 2 \operatorname{re}{\left(\operatorname{atan}{\left(- \frac{\sqrt{19}}{4} + \frac{\sqrt{3}}{4} + \frac{\sqrt{2} \sqrt{3 - \sqrt{57}}}{4} \right)}\right)} - 2 i \operatorname{im}{\left(\operatorname{atan}{\left(- \frac{\sqrt{19}}{4} + \frac{\sqrt{3}}{4} + \frac{\sqrt{2} \sqrt{3 - \sqrt{57}}}{4} \right)}\right)}\right) + \left(2 \operatorname{re}{\left(\operatorname{atan}{\left(- \frac{\sqrt{3}}{4} + \frac{\sqrt{19}}{4} + \frac{\sqrt{2} \sqrt{3 - \sqrt{57}}}{4} \right)}\right)} + 2 i \operatorname{im}{\left(\operatorname{atan}{\left(- \frac{\sqrt{3}}{4} + \frac{\sqrt{19}}{4} + \frac{\sqrt{2} \sqrt{3 - \sqrt{57}}}{4} \right)}\right)}\right)\right)\right) 
=
        /                          ____________\         /                          ____________\       /    /                            ____________\\       /    /                            ____________\\         /    /                            ____________\\         /    /                            ____________\\
        |  ___     ____     ___   /       ____ |         |  ___     ____     ___   /       ____ |       |    |    ____     ___     ___   /       ____ ||       |    |    ___     ____     ___   /       ____ ||         |    |    ____     ___     ___   /       ____ ||         |    |    ___     ____     ___   /       ____ ||
        |\/ 3    \/ 19    \/ 2 *\/  3 + \/ 57  |         |\/ 3    \/ 19    \/ 2 *\/  3 + \/ 57  |       |    |  \/ 19    \/ 3    \/ 2 *\/  3 - \/ 57  ||       |    |  \/ 3    \/ 19    \/ 2 *\/  3 - \/ 57  ||         |    |  \/ 19    \/ 3    \/ 2 *\/  3 - \/ 57  ||         |    |  \/ 3    \/ 19    \/ 2 *\/  3 - \/ 57  ||
- 2*atan|----- + ------ - ---------------------| - 2*atan|----- + ------ + ---------------------| - 2*re|atan|- ------ + ----- + ---------------------|| + 2*re|atan|- ----- + ------ + ---------------------|| - 2*I*im|atan|- ------ + ----- + ---------------------|| + 2*I*im|atan|- ----- + ------ + ---------------------||
        \  4       4                4          /         \  4       4                4          /       \    \    4        4               4          //       \    \    4       4                4          //         \    \    4        4               4          //         \    \    4       4                4          //
−2atan⁡(34+194+23+574)−2atan⁡(−23+574+34+194)−2re⁡(atan⁡(−194+34+23−574))+2re⁡(atan⁡(−34+194+23−574))−2iim⁡(atan⁡(−194+34+23−574))+2iim⁡(atan⁡(−34+194+23−574))- 2 \operatorname{atan}{\left(\frac{\sqrt{3}}{4} + \frac{\sqrt{19}}{4} + \frac{\sqrt{2} \sqrt{3 + \sqrt{57}}}{4} \right)} - 2 \operatorname{atan}{\left(- \frac{\sqrt{2} \sqrt{3 + \sqrt{57}}}{4} + \frac{\sqrt{3}}{4} + \frac{\sqrt{19}}{4} \right)} - 2 \operatorname{re}{\left(\operatorname{atan}{\left(- \frac{\sqrt{19}}{4} + \frac{\sqrt{3}}{4} + \frac{\sqrt{2} \sqrt{3 - \sqrt{57}}}{4} \right)}\right)} + 2 \operatorname{re}{\left(\operatorname{atan}{\left(- \frac{\sqrt{3}}{4} + \frac{\sqrt{19}}{4} + \frac{\sqrt{2} \sqrt{3 - \sqrt{57}}}{4} \right)}\right)} - 2 i \operatorname{im}{\left(\operatorname{atan}{\left(- \frac{\sqrt{19}}{4} + \frac{\sqrt{3}}{4} + \frac{\sqrt{2} \sqrt{3 - \sqrt{57}}}{4} \right)}\right)} + 2 i \operatorname{im}{\left(\operatorname{atan}{\left(- \frac{\sqrt{3}}{4} + \frac{\sqrt{19}}{4} + \frac{\sqrt{2} \sqrt{3 - \sqrt{57}}}{4} \right)}\right)} 
producto
/      /    /                            ____________\\         /    /                            ____________\\\ /    /    /                            ____________\\         /    /                            ____________\\\        /                          ____________\        /                          ____________\
|      |    |    ____     ___     ___   /       ____ ||         |    |    ____     ___     ___   /       ____ ||| |    |    |    ___     ____     ___   /       ____ ||         |    |    ___     ____     ___   /       ____ |||        |  ___     ____     ___   /       ____ |        |  ___     ____     ___   /       ____ |
|      |    |  \/ 19    \/ 3    \/ 2 *\/  3 - \/ 57  ||         |    |  \/ 19    \/ 3    \/ 2 *\/  3 - \/ 57  ||| |    |    |  \/ 3    \/ 19    \/ 2 *\/  3 - \/ 57  ||         |    |  \/ 3    \/ 19    \/ 2 *\/  3 - \/ 57  |||        |\/ 3    \/ 19    \/ 2 *\/  3 + \/ 57  |        |\/ 3    \/ 19    \/ 2 *\/  3 + \/ 57  |
|- 2*re|atan|- ------ + ----- + ---------------------|| - 2*I*im|atan|- ------ + ----- + ---------------------|||*|2*re|atan|- ----- + ------ + ---------------------|| + 2*I*im|atan|- ----- + ------ + ---------------------|||*-2*atan|----- + ------ + ---------------------|*-2*atan|----- + ------ - ---------------------|
\      \    \    4        4               4          //         \    \    4        4               4          /// \    \    \    4       4                4          //         \    \    4       4                4          ///        \  4       4                4          /        \  4       4                4          /
(−2re⁡(atan⁡(−194+34+23−574))−2iim⁡(atan⁡(−194+34+23−574)))(2re⁡(atan⁡(−34+194+23−574))+2iim⁡(atan⁡(−34+194+23−574)))(−2atan⁡(34+194+23+574))(−2atan⁡(−23+574+34+194))\left(- 2 \operatorname{re}{\left(\operatorname{atan}{\left(- \frac{\sqrt{19}}{4} + \frac{\sqrt{3}}{4} + \frac{\sqrt{2} \sqrt{3 - \sqrt{57}}}{4} \right)}\right)} - 2 i \operatorname{im}{\left(\operatorname{atan}{\left(- \frac{\sqrt{19}}{4} + \frac{\sqrt{3}}{4} + \frac{\sqrt{2} \sqrt{3 - \sqrt{57}}}{4} \right)}\right)}\right) \left(2 \operatorname{re}{\left(\operatorname{atan}{\left(- \frac{\sqrt{3}}{4} + \frac{\sqrt{19}}{4} + \frac{\sqrt{2} \sqrt{3 - \sqrt{57}}}{4} \right)}\right)} + 2 i \operatorname{im}{\left(\operatorname{atan}{\left(- \frac{\sqrt{3}}{4} + \frac{\sqrt{19}}{4} + \frac{\sqrt{2} \sqrt{3 - \sqrt{57}}}{4} \right)}\right)}\right) \left(- 2 \operatorname{atan}{\left(\frac{\sqrt{3}}{4} + \frac{\sqrt{19}}{4} + \frac{\sqrt{2} \sqrt{3 + \sqrt{57}}}{4} \right)}\right) \left(- 2 \operatorname{atan}{\left(- \frac{\sqrt{2} \sqrt{3 + \sqrt{57}}}{4} + \frac{\sqrt{3}}{4} + \frac{\sqrt{19}}{4} \right)}\right) 
=
    /    /    /                            ____________\\     /    /                            ____________\\\ /    /    /                            ____________\\     /    /                            ____________\\\     /                          ____________\     /                          ____________\
    |    |    |    ___     ____     ___   /       ____ ||     |    |    ___     ____     ___   /       ____ ||| |    |    |    ____     ___     ___   /       ____ ||     |    |    ____     ___     ___   /       ____ |||     |  ___     ____     ___   /       ____ |     |  ___     ____     ___   /       ____ |
    |    |    |  \/ 3    \/ 19    \/ 2 *\/  3 - \/ 57  ||     |    |  \/ 3    \/ 19    \/ 2 *\/  3 - \/ 57  ||| |    |    |  \/ 19    \/ 3    \/ 2 *\/  3 - \/ 57  ||     |    |  \/ 19    \/ 3    \/ 2 *\/  3 - \/ 57  |||     |\/ 3    \/ 19    \/ 2 *\/  3 + \/ 57  |     |\/ 3    \/ 19    \/ 2 *\/  3 + \/ 57  |
-16*|I*im|atan|- ----- + ------ + ---------------------|| + re|atan|- ----- + ------ + ---------------------|||*|I*im|atan|- ------ + ----- + ---------------------|| + re|atan|- ------ + ----- + ---------------------|||*atan|----- + ------ - ---------------------|*atan|----- + ------ + ---------------------|
    \    \    \    4       4                4          //     \    \    4       4                4          /// \    \    \    4        4               4          //     \    \    4        4               4          ///     \  4       4                4          /     \  4       4                4          /
−16(re⁡(atan⁡(−194+34+23−574))+iim⁡(atan⁡(−194+34+23−574)))(re⁡(atan⁡(−34+194+23−574))+iim⁡(atan⁡(−34+194+23−574)))atan⁡(34+194+23+574)atan⁡(−23+574+34+194)- 16 \left(\operatorname{re}{\left(\operatorname{atan}{\left(- \frac{\sqrt{19}}{4} + \frac{\sqrt{3}}{4} + \frac{\sqrt{2} \sqrt{3 - \sqrt{57}}}{4} \right)}\right)} + i \operatorname{im}{\left(\operatorname{atan}{\left(- \frac{\sqrt{19}}{4} + \frac{\sqrt{3}}{4} + \frac{\sqrt{2} \sqrt{3 - \sqrt{57}}}{4} \right)}\right)}\right) \left(\operatorname{re}{\left(\operatorname{atan}{\left(- \frac{\sqrt{3}}{4} + \frac{\sqrt{19}}{4} + \frac{\sqrt{2} \sqrt{3 - \sqrt{57}}}{4} \right)}\right)} + i \operatorname{im}{\left(\operatorname{atan}{\left(- \frac{\sqrt{3}}{4} + \frac{\sqrt{19}}{4} + \frac{\sqrt{2} \sqrt{3 - \sqrt{57}}}{4} \right)}\right)}\right) \operatorname{atan}{\left(\frac{\sqrt{3}}{4} + \frac{\sqrt{19}}{4} + \frac{\sqrt{2} \sqrt{3 + \sqrt{57}}}{4} \right)} \operatorname{atan}{\left(- \frac{\sqrt{2} \sqrt{3 + \sqrt{57}}}{4} + \frac{\sqrt{3}}{4} + \frac{\sqrt{19}}{4} \right)} 
-16*(i*im(atan(-sqrt(3)/4 + sqrt(19)/4 + sqrt(2)*sqrt(3 - sqrt(57))/4)) + re(atan(-sqrt(3)/4 + sqrt(19)/4 + sqrt(2)*sqrt(3 - sqrt(57))/4)))*(i*im(atan(-sqrt(19)/4 + sqrt(3)/4 + sqrt(2)*sqrt(3 - sqrt(57))/4)) + re(atan(-sqrt(19)/4 + sqrt(3)/4 + sqrt(2)*sqrt(3 - sqrt(57))/4)))*atan(sqrt(3)/4 + sqrt(19)/4 - sqrt(2)*sqrt(3 + sqrt(57))/4)*atan(sqrt(3)/4 + sqrt(19)/4 + sqrt(2)*sqrt(3 + sqrt(57))/4)
Respuesta rápida [src] 
           /    /                            ____________\\         /    /                            ____________\\
           |    |    ____     ___     ___   /       ____ ||         |    |    ____     ___     ___   /       ____ ||
           |    |  \/ 19    \/ 3    \/ 2 *\/  3 - \/ 57  ||         |    |  \/ 19    \/ 3    \/ 2 *\/  3 - \/ 57  ||
x1 = - 2*re|atan|- ------ + ----- + ---------------------|| - 2*I*im|atan|- ------ + ----- + ---------------------||
           \    \    4        4               4          //         \    \    4        4               4          //
x1=−2re⁡(atan⁡(−194+34+23−574))−2iim⁡(atan⁡(−194+34+23−574))x_{1} = - 2 \operatorname{re}{\left(\operatorname{atan}{\left(- \frac{\sqrt{19}}{4} + \frac{\sqrt{3}}{4} + \frac{\sqrt{2} \sqrt{3 - \sqrt{57}}}{4} \right)}\right)} - 2 i \operatorname{im}{\left(\operatorname{atan}{\left(- \frac{\sqrt{19}}{4} + \frac{\sqrt{3}}{4} + \frac{\sqrt{2} \sqrt{3 - \sqrt{57}}}{4} \right)}\right)} 
         /    /                            ____________\\         /    /                            ____________\\
         |    |    ___     ____     ___   /       ____ ||         |    |    ___     ____     ___   /       ____ ||
         |    |  \/ 3    \/ 19    \/ 2 *\/  3 - \/ 57  ||         |    |  \/ 3    \/ 19    \/ 2 *\/  3 - \/ 57  ||
x2 = 2*re|atan|- ----- + ------ + ---------------------|| + 2*I*im|atan|- ----- + ------ + ---------------------||
         \    \    4       4                4          //         \    \    4       4                4          //
x2=2re⁡(atan⁡(−34+194+23−574))+2iim⁡(atan⁡(−34+194+23−574))x_{2} = 2 \operatorname{re}{\left(\operatorname{atan}{\left(- \frac{\sqrt{3}}{4} + \frac{\sqrt{19}}{4} + \frac{\sqrt{2} \sqrt{3 - \sqrt{57}}}{4} \right)}\right)} + 2 i \operatorname{im}{\left(\operatorname{atan}{\left(- \frac{\sqrt{3}}{4} + \frac{\sqrt{19}}{4} + \frac{\sqrt{2} \sqrt{3 - \sqrt{57}}}{4} \right)}\right)} 
            /                          ____________\
            |  ___     ____     ___   /       ____ |
            |\/ 3    \/ 19    \/ 2 *\/  3 + \/ 57  |
x3 = -2*atan|----- + ------ + ---------------------|
            \  4       4                4          /
x3=−2atan⁡(34+194+23+574)x_{3} = - 2 \operatorname{atan}{\left(\frac{\sqrt{3}}{4} + \frac{\sqrt{19}}{4} + \frac{\sqrt{2} \sqrt{3 + \sqrt{57}}}{4} \right)} 
            /                          ____________\
            |  ___     ____     ___   /       ____ |
            |\/ 3    \/ 19    \/ 2 *\/  3 + \/ 57  |
x4 = -2*atan|----- + ------ - ---------------------|
            \  4       4                4          /
x4=−2atan⁡(−23+574+34+194)x_{4} = - 2 \operatorname{atan}{\left(- \frac{\sqrt{2} \sqrt{3 + \sqrt{57}}}{4} + \frac{\sqrt{3}}{4} + \frac{\sqrt{19}}{4} \right)} 
x4 = -2*atan(-sqrt(2)*sqrt(3 + sqrt(57))/4 + sqrt(3)/4 + sqrt(19)/4)
Respuesta numérica [src] 
x1 = 36.9826612839022
x2 = 74.6817731269797
x3 = -82.39785955251
x4 = 24.416290669543
x5 = 54.1235256702018
x6 = 99.814514355698
x7 = -50.981933016612
x8 = -84.1065510877491
x9 = -90.3897363949286
x10 = -44.6987477094325
x11 = -71.5401804733899
x12 = -38.4155624022529
x13 = -63.5483036309712
x14 = -46.4074392446715
x15 = -27.5578833231328
x16 = 28.9907844414835
x17 = 68.3985878198001
x18 = 16.4244138271243
x19 = 35.2739697486631
x20 = -6939.06172122068
x21 = 30.6994759767226
x22 = -33.8410686303124
x23 = -76.1146742453304
x24 = 41.5571550558427
x25 = -96.6729217021082
x26 = -57.2651183237916
x27 = 18.1331053623634
x28 = 93.5313290485184
x29 = -52.6906245518511
x30 = -13.2828211735345
x31 = -88.6810448596896
x32 = 85.5394522060998
x33 = 43.2658465910818
x34 = 10.1412285199447
x35 = 91.8226375132794
x36 = 11.8499200551838
x37 = -32.1323770950733
x38 = 5.56673474800423
x39 = -101.247415474049
x40 = -58.9738098590307
x41 = 55.8322172054409
x42 = 22.7075991343039
x43 = -65.2569951662103
x44 = 47.8403403630222
x45 = 3.85804321276515
x46 = 60.4067109773814
x47 = -19.5660064807141
x48 = 79.2562668989202
x49 = 72.9730815917406
x50 = 49.5490318982613
x51 = 87.2481437413389
x52 = -25.8491917878937
x53 = 80.9649584341593
x54 = -77.8233657805695
x55 = -94.9642301668692
x56 = 98.1058228204589
x57 = -69.8314889381508
x58 = -8.70832740159403
x59 = -0.716450559175354
x60 = -6.99963586635494
x61 = 66.689896284561
x62 = 62.1154025126205
x63 = -2.42514209441444
x64 = -40.124253937492
x65 = -21.2746980159532
x65 = -21.2746980159532
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