Question
$$x^2+(x+11)^2 = 169$$
Answer
$$ \begin{matrix}x_1 = -\dfrac{ 11 }{ 2 }-\dfrac{\sqrt{ 217 }}{ 2 } & x_2 = -\dfrac{ 11 }{ 2 }+\dfrac{\sqrt{ 217 }}{ 2 } \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} x^2+(x+11)^2 &= 169&& \text{simplify left side} \\[1 em]x^2+x^2+22x+121 &= 169&& \\[1 em]2x^2+22x+121 &= 169&& \text{move all terms to the left hand side } \\[1 em]2x^2+22x+121-169 &= 0&& \text{simplify left side} \\[1 em]2x^2+22x-48 &= 0&& \\[1 em] \end{aligned} $$
$ 2x^{2}+22x-48 = 0 $ is a quadratic equation.
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