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sqrt(2(x+6))=6-3^sqrt(x+6) la ecuación

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Solución numérica:

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Solución

Ha introducido [src] 
                       _______
  ___________        \/ x + 6 
\/ 2*(x + 6)  = 6 - 3
2(x+6)=6−3x+6\sqrt{2 \left(x + 6\right)} = 6 - 3^{\sqrt{x + 6}}
Simplificar
Gráfica
012345-6-5-4-3-2-1-5050
Trazar el gráfico f1(x)
Trazar el gráfico f2(x)
Suma y producto de raíces [src] 
suma
                                                 2
     /   /          ___       \                 \ 
     |   |  ___   \/ 2        |                 | 
     |   |\/ 2 *27     *log(3)|       ___       | 
     |- W|--------------------| + 3*\/ 2 *log(3)| 
     \   \         2          /                 / 
-6 + ---------------------------------------------
                           2                      
                        log (3)
−6+(−W(2⋅272log⁡(3)2)+32log⁡(3))2log⁡(3)2-6 + \frac{\left(- W\left(\frac{\sqrt{2} \cdot 27^{\sqrt{2}} \log{\left(3 \right)}}{2}\right) + 3 \sqrt{2} \log{\left(3 \right)}\right)^{2}}{\log{\left(3 \right)}^{2}} 
=
                                                 2
     /   /          ___       \                 \ 
     |   |  ___   \/ 2        |                 | 
     |   |\/ 2 *27     *log(3)|       ___       | 
     |- W|--------------------| + 3*\/ 2 *log(3)| 
     \   \         2          /                 / 
-6 + ---------------------------------------------
                           2                      
                        log (3)
−6+(−W(2⋅272log⁡(3)2)+32log⁡(3))2log⁡(3)2-6 + \frac{\left(- W\left(\frac{\sqrt{2} \cdot 27^{\sqrt{2}} \log{\left(3 \right)}}{2}\right) + 3 \sqrt{2} \log{\left(3 \right)}\right)^{2}}{\log{\left(3 \right)}^{2}} 
producto
                                                 2
     /   /          ___       \                 \ 
     |   |  ___   \/ 2        |                 | 
     |   |\/ 2 *27     *log(3)|       ___       | 
     |- W|--------------------| + 3*\/ 2 *log(3)| 
     \   \         2          /                 / 
-6 + ---------------------------------------------
                           2                      
                        log (3)
−6+(−W(2⋅272log⁡(3)2)+32log⁡(3))2log⁡(3)2-6 + \frac{\left(- W\left(\frac{\sqrt{2} \cdot 27^{\sqrt{2}} \log{\left(3 \right)}}{2}\right) + 3 \sqrt{2} \log{\left(3 \right)}\right)^{2}}{\log{\left(3 \right)}^{2}} 
=
                                                 2
     /   /          ___       \                 \ 
     |   |  ___   \/ 2        |                 | 
     |   |\/ 2 *27     *log(3)|       ___       | 
     |- W|--------------------| + 3*\/ 2 *log(3)| 
     \   \         2          /                 / 
-6 + ---------------------------------------------
                           2                      
                        log (3)
−6+(−W(2⋅272log⁡(3)2)+32log⁡(3))2log⁡(3)2-6 + \frac{\left(- W\left(\frac{\sqrt{2} \cdot 27^{\sqrt{2}} \log{\left(3 \right)}}{2}\right) + 3 \sqrt{2} \log{\left(3 \right)}\right)^{2}}{\log{\left(3 \right)}^{2}} 
-6 + (-LambertW(sqrt(2)*27^(sqrt(2))*log(3)/2) + 3*sqrt(2)*log(3))^2/log(3)^2
Respuesta rápida [src] 
                                                      2
          /   /          ___       \                 \ 
          |   |  ___   \/ 2        |                 | 
          |   |\/ 2 *27     *log(3)|       ___       | 
          |- W|--------------------| + 3*\/ 2 *log(3)| 
          \   \         2          /                 / 
x1 = -6 + ---------------------------------------------
                                2                      
                             log (3)
x1=−6+(−W(2⋅272log⁡(3)2)+32log⁡(3))2log⁡(3)2x_{1} = -6 + \frac{\left(- W\left(\frac{\sqrt{2} \cdot 27^{\sqrt{2}} \log{\left(3 \right)}}{2}\right) + 3 \sqrt{2} \log{\left(3 \right)}\right)^{2}}{\log{\left(3 \right)}^{2}} 
x1 = -6 + (-LambertW(sqrt(2)*27^(sqrt(2))*log(3)/2) + 3*sqrt(2)*log(3))^2/log(3)^2
Respuesta numérica [src] 
x1 = -4.31418209003972
x2 = -24.9090844732826 - 17.302412468094*i
x3 = -24.9090844732826 + 17.302412468094*i
x3 = -24.9090844732826 + 17.302412468094*i
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