$$(w+7)^2 = 2w^2+23w+69$$
Answer
$$ \begin{matrix}w_1 = -4 & w_2 = -5 \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} (w+7)^2 &= 2w^2+23w+69&& \text{simplify left side} \\[1 em]w^2+14w+49 &= 2w^2+23w+69&& \text{move all terms to the left hand side } \\[1 em]w^2+14w+49-2w^2-23w-69 &= 0&& \text{simplify left side} \\[1 em]-w^2-9w-20 &= 0&& \\[1 em] \end{aligned} $$
$ -x^{2}-9x-20 = 0 $ is a quadratic equation.
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