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tan(a)=x/37-6.78 la ecuación

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Solución numérica:

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Solución

Ha introducido [src] 
         x    339
tan(a) = -- - ---
         37    50
tan⁡(a)=x37−33950\tan{\left(a \right)} = \frac{x}{37} - \frac{339}{50}
Simplificar
Solución detallada
Tenemos la ecuación
tan⁡(a)=x37−33950\tan{\left(a \right)} = \frac{x}{37} - \frac{339}{50}
cambiamos
−x37+tan⁡(a)+28950=0- \frac{x}{37} + \tan{\left(a \right)} + \frac{289}{50} = 0
−x37+tan⁡(a)+28950=0- \frac{x}{37} + \tan{\left(a \right)} + \frac{289}{50} = 0
Sustituimos
w=tan⁡(a)w = \tan{\left(a \right)}
Transportamos los términos libres (sin w)
del miembro izquierdo al derecho, obtenemos:
w−x37=−28950w - \frac{x}{37} = - \frac{289}{50}
Move the summands with the other variables
del miembro izquierdo al derecho, obtenemos:
w=x37−28950w = \frac{x}{37} - \frac{289}{50}
Obtenemos la respuesta: w = -289/50 + x/37
hacemos cambio inverso
tan⁡(a)=w\tan{\left(a \right)} = w
sustituimos w:
Gráfica
Suma y producto de raíces [src] 
suma
12543         37*sin(2*re(a))               37*I*sinh(2*im(a))     
----- + ---------------------------- + ----------------------------
  50    cos(2*re(a)) + cosh(2*im(a))   cos(2*re(a)) + cosh(2*im(a))
1254350+37sin⁡(2re⁡(a))cos⁡(2re⁡(a))+cosh⁡(2im⁡(a))+37isinh⁡(2im⁡(a))cos⁡(2re⁡(a))+cosh⁡(2im⁡(a))\frac{12543}{50} + \frac{37 \sin{\left(2 \operatorname{re}{\left(a\right)} \right)}}{\cos{\left(2 \operatorname{re}{\left(a\right)} \right)} + \cosh{\left(2 \operatorname{im}{\left(a\right)} \right)}} + \frac{37 i \sinh{\left(2 \operatorname{im}{\left(a\right)} \right)}}{\cos{\left(2 \operatorname{re}{\left(a\right)} \right)} + \cosh{\left(2 \operatorname{im}{\left(a\right)} \right)}} 
=
12543         37*sin(2*re(a))               37*I*sinh(2*im(a))     
----- + ---------------------------- + ----------------------------
  50    cos(2*re(a)) + cosh(2*im(a))   cos(2*re(a)) + cosh(2*im(a))
1254350+37sin⁡(2re⁡(a))cos⁡(2re⁡(a))+cosh⁡(2im⁡(a))+37isinh⁡(2im⁡(a))cos⁡(2re⁡(a))+cosh⁡(2im⁡(a))\frac{12543}{50} + \frac{37 \sin{\left(2 \operatorname{re}{\left(a\right)} \right)}}{\cos{\left(2 \operatorname{re}{\left(a\right)} \right)} + \cosh{\left(2 \operatorname{im}{\left(a\right)} \right)}} + \frac{37 i \sinh{\left(2 \operatorname{im}{\left(a\right)} \right)}}{\cos{\left(2 \operatorname{re}{\left(a\right)} \right)} + \cosh{\left(2 \operatorname{im}{\left(a\right)} \right)}} 
producto
12543         37*sin(2*re(a))               37*I*sinh(2*im(a))     
----- + ---------------------------- + ----------------------------
  50    cos(2*re(a)) + cosh(2*im(a))   cos(2*re(a)) + cosh(2*im(a))
1254350+37sin⁡(2re⁡(a))cos⁡(2re⁡(a))+cosh⁡(2im⁡(a))+37isinh⁡(2im⁡(a))cos⁡(2re⁡(a))+cosh⁡(2im⁡(a))\frac{12543}{50} + \frac{37 \sin{\left(2 \operatorname{re}{\left(a\right)} \right)}}{\cos{\left(2 \operatorname{re}{\left(a\right)} \right)} + \cosh{\left(2 \operatorname{im}{\left(a\right)} \right)}} + \frac{37 i \sinh{\left(2 \operatorname{im}{\left(a\right)} \right)}}{\cos{\left(2 \operatorname{re}{\left(a\right)} \right)} + \cosh{\left(2 \operatorname{im}{\left(a\right)} \right)}} 
=
37*(50*sin(2*re(a)) + 339*cos(2*re(a)) + 339*cosh(2*im(a)) + 50*I*sinh(2*im(a)))
--------------------------------------------------------------------------------
                       50*(cos(2*re(a)) + cosh(2*im(a)))
37(50sin⁡(2re⁡(a))+339cos⁡(2re⁡(a))+50isinh⁡(2im⁡(a))+339cosh⁡(2im⁡(a)))50(cos⁡(2re⁡(a))+cosh⁡(2im⁡(a)))\frac{37 \left(50 \sin{\left(2 \operatorname{re}{\left(a\right)} \right)} + 339 \cos{\left(2 \operatorname{re}{\left(a\right)} \right)} + 50 i \sinh{\left(2 \operatorname{im}{\left(a\right)} \right)} + 339 \cosh{\left(2 \operatorname{im}{\left(a\right)} \right)}\right)}{50 \left(\cos{\left(2 \operatorname{re}{\left(a\right)} \right)} + \cosh{\left(2 \operatorname{im}{\left(a\right)} \right)}\right)} 
37*(50*sin(2*re(a)) + 339*cos(2*re(a)) + 339*cosh(2*im(a)) + 50*i*sinh(2*im(a)))/(50*(cos(2*re(a)) + cosh(2*im(a))))
Respuesta rápida [src] 
     12543         37*sin(2*re(a))               37*I*sinh(2*im(a))     
x1 = ----- + ---------------------------- + ----------------------------
       50    cos(2*re(a)) + cosh(2*im(a))   cos(2*re(a)) + cosh(2*im(a))
x1=1254350+37sin⁡(2re⁡(a))cos⁡(2re⁡(a))+cosh⁡(2im⁡(a))+37isinh⁡(2im⁡(a))cos⁡(2re⁡(a))+cosh⁡(2im⁡(a))x_{1} = \frac{12543}{50} + \frac{37 \sin{\left(2 \operatorname{re}{\left(a\right)} \right)}}{\cos{\left(2 \operatorname{re}{\left(a\right)} \right)} + \cosh{\left(2 \operatorname{im}{\left(a\right)} \right)}} + \frac{37 i \sinh{\left(2 \operatorname{im}{\left(a\right)} \right)}}{\cos{\left(2 \operatorname{re}{\left(a\right)} \right)} + \cosh{\left(2 \operatorname{im}{\left(a\right)} \right)}} 
x1 = 12543/50 + 37*sin(2*re(a))/(cos(2*re(a)) + cosh(2*im(a))) + 37*i*sinh(2*im(a))/(cos(2*re(a)) + cosh(2*im(a)))
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