# How do you solve 5+2sqrt(5x+32)=12 and identify any restrictions?

#### Answer:

$x = - \frac{79}{20}$

#### Explanation:

$5 + 2 \sqrt{5 x + 32} = 12$
$2 \sqrt{5 x + 32} = 7$
$\sqrt{5 x + 32} = \frac{7}{2}$
$5 x + 32 = \pm {\left(\frac{7}{2}\right)}^{2}$
$5 x = \pm {\left(\frac{7}{2}\right)}^{2} - 32$
$x = \frac{1}{5} \left(\pm \frac{49}{4} - 32\right)$
$x = - \frac{79}{20} , - \frac{177}{20}$

Plug them into the equation and check:
1.-79/20
$5 + 2 \sqrt{5 \cdot - \frac{79}{20} + 32} = 12$
$5 + 2 \sqrt{\frac{49}{4}} = 12$
$5 + 2 \cdot \frac{7}{2} = 12$
$5 + 7 = 12$
$12 = 12$
(This one works)

2.-177/20
$5 + 2 \sqrt{5 \cdot - \frac{177}{20} + 32} = 12$
$5 + 2 \sqrt{- \frac{49}{4}} = 12$
(This one doesn't work since you can't have a negative square)