# How do you solve (3x+2)^2=9?

Jul 6, 2016

$x = \frac{1}{3} , - \frac{5}{3}$ These are all of the solutions, but if you consider only the positive square root, then $x = \frac{1}{3}$ is the solution.

#### Explanation:

Take the square root of both sides

$\sqrt{{\left(3 x + 2\right)}^{2}} = \sqrt{9}$

The square root of a value squared is that value and the square root of 9 is 3 and -3.

a) $3 x + 2 = 3$
b) $3 x + 2 = - 3$

We have two equations since there are two values for the square root of 9. Isolate the variable and solve for $x$.

a) $3 x = 1$
$x = \frac{1}{3}$

b) $3 x = - 5$
$x = - \frac{5}{3}$

Solutions are: $x = \frac{1}{3} , - \frac{5}{3}$