Solve: $x^{2} + (20 - x)^{2} = 218$ .

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Solution

$x^{2} + (20 - x)^{2} = 218.$
$x^{2} + 400 + x^{2} - 40 x = 218.$
$2 x^{2} - 40 x + 182 = 0$
$x^{2} - 20 x + 91 = 0.$
$(x - 13) (x - 7) = 0$
$x = 13, 7$

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