# How do you solve by completing the square x=sqrt(x+13)+7?

Apr 2, 2015

x=3; x=12

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

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

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