Solve the equation : ${(x^{2} + 12 x)}^{2} + 35 (x^{2} + 12 x) + 150 = 0$

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Solution

$\begin{matrix} {(x^{2} + 12 x)}^{2} + 35 (x^{2} + 12 x) + 150 = 0 t^{2} + 35 t + 150 = 0 (t + 30) (t + 5) t = - 5 t = - 30 x^{2} + 12 x + 5 = 0 o r x^{2} + 12 x + 30 = 0 x = \frac{- 12 \pm \sqrt{144 - 20}}{2} x = \frac{- 12 \pm \sqrt{144 - 120}}{2} = \frac{- 12 \pm 2 \sqrt{13}}{2} x = \frac{- 12 \pm 2 \sqrt{6}}{2} x = - 6 \pm \sqrt{31} o r x = - 6 \pm \sqrt{6} \end{matrix}$

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