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cospi(4x+132)/4=-sqrt(2)/2 la ecuación

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Solución numérica:

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Solución

Ha introducido [src]
                          ___ 
cos(p)*I*(4*x + 132)   -\/ 2  
-------------------- = -------
         4                2   
$$\frac{i \cos{\left(p \right)} \left(4 x + 132\right)}{4} = \frac{\left(-1\right) \sqrt{2}}{2}$$
Solución detallada
Tenemos la ecuación
$$\frac{i \cos{\left(p \right)} \left(4 x + 132\right)}{4} = \frac{\left(-1\right) \sqrt{2}}{2}$$
cambiamos
$$i \left(x + 33\right) \cos{\left(p \right)} - 1 + \frac{\sqrt{2}}{2} = 0$$
$$\frac{i \cos{\left(p \right)} \left(4 x + 132\right)}{4} - 1 - \frac{\left(-1\right) \sqrt{2}}{2} = 0$$
Sustituimos
$$w = \cos{\left(p \right)}$$
Abrimos los paréntesis en el miembro izquierdo de la ecuación
-1 - -sqrt+2)/2 + i*w4*x/4+132/4 = 0

Sumamos los términos semejantes en el miembro izquierdo de la ecuación:
-1 + sqrt(2)/2 + i*w*(132 + 4*x)/4 = 0

Transportamos los términos libres (sin w)
del miembro izquierdo al derecho, obtenemos:
$$\frac{i w \left(4 x + 132\right)}{4} + \frac{\sqrt{2}}{2} = 1$$
Dividamos ambos miembros de la ecuación en (sqrt(2)/2 + i*w*(132 + 4*x)/4)/w
w = 1 / ((sqrt(2)/2 + i*w*(132 + 4*x)/4)/w)

Obtenemos la respuesta: w = i*(-2 + sqrt(2))/(2*(33 + x))
hacemos cambio inverso
$$\cos{\left(p \right)} = w$$
sustituimos w:
Gráfica
Respuesta rápida [src]
                           ___                                                        ___                                   
                         \/ 2 *sin(re(p))*sinh(im(p))                             I*\/ 2 *cos(re(p))*cosh(im(p))            
x1 = -33 - ------------------------------------------------------- + -------------------------------------------------------
             /   2            2             2            2       \     /   2            2             2            2       \
           2*\cos (re(p))*cosh (im(p)) + sin (re(p))*sinh (im(p))/   2*\cos (re(p))*cosh (im(p)) + sin (re(p))*sinh (im(p))/
$$x_{1} = -33 - \frac{\sqrt{2} \sin{\left(\operatorname{re}{\left(p\right)} \right)} \sinh{\left(\operatorname{im}{\left(p\right)} \right)}}{2 \left(\sin^{2}{\left(\operatorname{re}{\left(p\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(p\right)} \right)} + \cos^{2}{\left(\operatorname{re}{\left(p\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(p\right)} \right)}\right)} + \frac{\sqrt{2} i \cos{\left(\operatorname{re}{\left(p\right)} \right)} \cosh{\left(\operatorname{im}{\left(p\right)} \right)}}{2 \left(\sin^{2}{\left(\operatorname{re}{\left(p\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(p\right)} \right)} + \cos^{2}{\left(\operatorname{re}{\left(p\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(p\right)} \right)}\right)}$$
x1 = -33 - sqrt(2)*sin(re(p))*sinh(im(p))/(2*(sin(re(p))^2*sinh(im(p))^2 + cos(re(p))^2*cosh(im(p))^2)) + sqrt(2)*i*cos(re(p))*cosh(im(p))/(2*(sin(re(p))^2*sinh(im(p))^2 + cos(re(p))^2*cosh(im(p))^2))
Suma y producto de raíces [src]
suma
                      ___                                                        ___                                   
                    \/ 2 *sin(re(p))*sinh(im(p))                             I*\/ 2 *cos(re(p))*cosh(im(p))            
-33 - ------------------------------------------------------- + -------------------------------------------------------
        /   2            2             2            2       \     /   2            2             2            2       \
      2*\cos (re(p))*cosh (im(p)) + sin (re(p))*sinh (im(p))/   2*\cos (re(p))*cosh (im(p)) + sin (re(p))*sinh (im(p))/
$$-33 - \frac{\sqrt{2} \sin{\left(\operatorname{re}{\left(p\right)} \right)} \sinh{\left(\operatorname{im}{\left(p\right)} \right)}}{2 \left(\sin^{2}{\left(\operatorname{re}{\left(p\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(p\right)} \right)} + \cos^{2}{\left(\operatorname{re}{\left(p\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(p\right)} \right)}\right)} + \frac{\sqrt{2} i \cos{\left(\operatorname{re}{\left(p\right)} \right)} \cosh{\left(\operatorname{im}{\left(p\right)} \right)}}{2 \left(\sin^{2}{\left(\operatorname{re}{\left(p\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(p\right)} \right)} + \cos^{2}{\left(\operatorname{re}{\left(p\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(p\right)} \right)}\right)}$$
=
                      ___                                                        ___                                   
                    \/ 2 *sin(re(p))*sinh(im(p))                             I*\/ 2 *cos(re(p))*cosh(im(p))            
-33 - ------------------------------------------------------- + -------------------------------------------------------
        /   2            2             2            2       \     /   2            2             2            2       \
      2*\cos (re(p))*cosh (im(p)) + sin (re(p))*sinh (im(p))/   2*\cos (re(p))*cosh (im(p)) + sin (re(p))*sinh (im(p))/
$$-33 - \frac{\sqrt{2} \sin{\left(\operatorname{re}{\left(p\right)} \right)} \sinh{\left(\operatorname{im}{\left(p\right)} \right)}}{2 \left(\sin^{2}{\left(\operatorname{re}{\left(p\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(p\right)} \right)} + \cos^{2}{\left(\operatorname{re}{\left(p\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(p\right)} \right)}\right)} + \frac{\sqrt{2} i \cos{\left(\operatorname{re}{\left(p\right)} \right)} \cosh{\left(\operatorname{im}{\left(p\right)} \right)}}{2 \left(\sin^{2}{\left(\operatorname{re}{\left(p\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(p\right)} \right)} + \cos^{2}{\left(\operatorname{re}{\left(p\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(p\right)} \right)}\right)}$$
producto
                      ___                                                        ___                                   
                    \/ 2 *sin(re(p))*sinh(im(p))                             I*\/ 2 *cos(re(p))*cosh(im(p))            
-33 - ------------------------------------------------------- + -------------------------------------------------------
        /   2            2             2            2       \     /   2            2             2            2       \
      2*\cos (re(p))*cosh (im(p)) + sin (re(p))*sinh (im(p))/   2*\cos (re(p))*cosh (im(p)) + sin (re(p))*sinh (im(p))/
$$-33 - \frac{\sqrt{2} \sin{\left(\operatorname{re}{\left(p\right)} \right)} \sinh{\left(\operatorname{im}{\left(p\right)} \right)}}{2 \left(\sin^{2}{\left(\operatorname{re}{\left(p\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(p\right)} \right)} + \cos^{2}{\left(\operatorname{re}{\left(p\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(p\right)} \right)}\right)} + \frac{\sqrt{2} i \cos{\left(\operatorname{re}{\left(p\right)} \right)} \cosh{\left(\operatorname{im}{\left(p\right)} \right)}}{2 \left(\sin^{2}{\left(\operatorname{re}{\left(p\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(p\right)} \right)} + \cos^{2}{\left(\operatorname{re}{\left(p\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(p\right)} \right)}\right)}$$
=
 /  /  ___                            \                            \ 
 |  |\/ 2                             |                            | 
-|I*|----- + 33*sin(re(p))*sinh(im(p))| - 33*cos(re(p))*cosh(im(p))| 
 \  \  2                              /                            / 
---------------------------------------------------------------------
          -cos(re(p))*cosh(im(p)) + I*sin(re(p))*sinh(im(p))         
$$- \frac{i \left(33 \sin{\left(\operatorname{re}{\left(p\right)} \right)} \sinh{\left(\operatorname{im}{\left(p\right)} \right)} + \frac{\sqrt{2}}{2}\right) - 33 \cos{\left(\operatorname{re}{\left(p\right)} \right)} \cosh{\left(\operatorname{im}{\left(p\right)} \right)}}{i \sin{\left(\operatorname{re}{\left(p\right)} \right)} \sinh{\left(\operatorname{im}{\left(p\right)} \right)} - \cos{\left(\operatorname{re}{\left(p\right)} \right)} \cosh{\left(\operatorname{im}{\left(p\right)} \right)}}$$
-(i*(sqrt(2)/2 + 33*sin(re(p))*sinh(im(p))) - 33*cos(re(p))*cosh(im(p)))/(-cos(re(p))*cosh(im(p)) + i*sin(re(p))*sinh(im(p)))