How do you solve by completing the square $x = \sqrt{x + 13} + 7$ $x=sqrt(x+13)+7$ ?

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How do you solve by completing the square $x = \sqrt{x + 13} + 7$ $x=sqrt(x+13)+7$ ?

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Answer 1 · 2015-04-02T15:11:18

x=3; x=12

Rewrite it as x-7= $\sqrt{x + 13}$ $sqrt(x+13)$ . Then square both sides and simplify,

$x^{2}$ $x^2$ - 14x +49= x+13

$x^{2}$ $x^2$ -15x +36=0
$x^{2}$ $x^2$ -15x + $\frac{225}{4}$ $225/4$ - $\frac{225}{4}$ $225/4$ +36=0
(x- $\frac{15}{2}$ $15/2$ )^2= $\frac{81}{4}$ $81/4$
x- $\frac{15}{2}$ $15/2$ = $\frac{9}{2}$ $9/2$ or $- \frac{9}{2}$ $-9/2$
x= $\frac{15}{2}$ $15/2$ + $\frac{9}{2}$ $9/2$ or $\frac{15}{2}$ $15/2$ - $\frac{9}{2}$ $9/2$
x= 12 or 3

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How do you solve by completing the square $x = \sqrt{x + 13} + 7$ $x=sqrt(x+13)+7$ ?

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How do you solve by completing the square $x = \sqrt{x + 13} + 7$ $x=sqrt(x+13)+7$ ?