Question
$$(x+1)^2+(x-8)^2 = 50$$
Answer
$$ \begin{matrix}x_1 = \dfrac{ 7 }{ 2 }-\dfrac{\sqrt{ 19 }}{ 2 } & x_2 = \dfrac{ 7 }{ 2 }+\dfrac{\sqrt{ 19 }}{ 2 } \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} (x+1)^2+(x-8)^2 &= 50&& \text{simplify left side} \\[1 em]x^2+2x+1+x^2-16x+64 &= 50&& \\[1 em]2x^2-14x+65 &= 50&& \text{move all terms to the left hand side } \\[1 em]2x^2-14x+65-50 &= 0&& \text{simplify left side} \\[1 em]2x^2-14x+15 &= 0&& \\[1 em] \end{aligned} $$
$ 2x^{2}-14x+15 = 0 $ is a quadratic equation.
You can use step-by-step quadratic equation solver to see a detailed explanation on how to solve this equation.
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