Question
$$2(x+2)^2-5 = 8$$
Answer
$$ \begin{matrix}x_1 = -2-\dfrac{\sqrt{ 26 }}{ 2 } & x_2 = -2+\dfrac{\sqrt{ 26 }}{ 2 } \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} 2(x+2)^2-5 &= 8&& \text{simplify left side} \\[1 em]2(x^2+4x+4)-5 &= 8&& \\[1 em]2x^2+8x+8-5 &= 8&& \\[1 em]2x^2+8x+3 &= 8&& \text{move all terms to the left hand side } \\[1 em]2x^2+8x+3-8 &= 0&& \text{simplify left side} \\[1 em]2x^2+8x-5 &= 0&& \\[1 em] \end{aligned} $$
$ 2x^{2}+8x-5 = 0 $ is a quadratic equation.
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