# How do you solve sqrt(2x +3) = 6-x?

Apr 4, 2018

$x = 3$

#### Explanation:

$\sqrt{2 x + 3} = 6 - x$

Square both sides:

${\sqrt{2 x + 3}}^{2} = {\left(6 - x\right)}^{2}$

Notice that $2 x + 3 \ge 0$ and $6 - x \ge 0$
$\implies - \frac{3}{2} \le x \le 6$

$2 x + 3 = 36 - 12 x + {x}^{2}$

${x}^{2} - 14 x + 33 = 0$

$\left(x - 11\right) \left(x - 3\right) = 0$

$x = 3 , 11$

Since $- \frac{3}{2} \le x \le 6$ , $x = 11$ will not work in the original eqaution and the answer is $x = 3$.