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Factor Theorem

Solve for x...

Question

Solve for $x$ :
$x^{2} + (x + 1)^{2} = 365$

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Solution

Now,

$x^{2} + (x + 1)^{2} = 365$

or, $x^{2} + (x^{2} + 2 x + 1) = 365$

or, $2 x^{2} + 2 x - 364 = 0$

or, $x^{2} + x - 182 = 0$

or, $x^{2} + 14 x - 13 x - 182 = 0$

or, $x (x + 14) - 13 (x + 14) = 0$

or, $(x + 14) (x - 13) = 0$

or, $x = 13, - 14$ .

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