# How do you solve sqrt (x+9)=4?

Jan 27, 2016

To solve equations that involve radicals, you must square both sides of the equation.

#### Explanation:

$\sqrt{x + 9}$ = 4

${\left(\sqrt{x + 9}\right)}^{2} = {\left(4\right)}^{2}$

x + 9 = 16

x = 16 - 9

x = 7

With radical equations it is alway vital to check your solutions in the original equation, since extraneous solutions may arise. You must especially be careful of them in radical-quadratic equations, where two solutions often appear but oftentimes only one is the correct solution.

Practice exercises:

1. Solve each equation. Watch out for extraneous solutions.

a) $\sqrt{2 x + 5}$ = 7

b) $\sqrt{3 x + 1}$ = x - 3

c) $\sqrt{2 x + 2}$ - $\sqrt{x + 2}$ = 1

Jan 30, 2016

$x = 7$

#### Explanation:

$\sqrt{x + 9} = 4$

Square both sides:

$\rightarrow {\left(\sqrt{x + 9}\right)}^{2} = {4}^{2}$

$\rightarrow x + 9 = 16$

$\rightarrow x = 16 - 9 = 7$