Solve Using the Square Root Property (3x+7)^2=36

${(3 x + 7)}^{2} = 36$

Step 1

Take the specified root of both sides of the equation to eliminate the exponent on the left side.

$3 x + 7 = \pm \sqrt{36}$

Step 2

Simplify $\pm \sqrt{36}$ .

Rewrite $36$ as $6^{2}$ .

$3 x + 7 = \pm \sqrt{6^{2}}$

Pull terms out from under the radical, assuming positive real numbers.

$3 x + 7 = \pm 6$

Step 3

The complete solution is the result of both the positive and negative portions of the solution.

First, use the positive value of the $\pm$ to find the first solution.

$3 x + 7 = 6$

Move all terms not containing $x$ to the right side of the equation.

Subtract $7$ from both sides of the equation.

$3 x = 6 - 7$

Subtract $7$ from $6$ .

$3 x = - 1$

Divide each term in $3 x = - 1$ by $3$ and simplify.

Divide each term in $3 x = - 1$ by $3$ .

$\frac{3 x}{3} = \frac{- 1}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 x}{3} = \frac{- 1}{3}$

Divide $x$ by $1$ .

$x = \frac{- 1}{3}$

Simplify the right side.

Move the negative in front of the fraction.

$x = - \frac{1}{3}$

Next, use the negative value of the $\pm$ to find the second solution.

$3 x + 7 = - 6$

Move all terms not containing $x$ to the right side of the equation.

Subtract $7$ from both sides of the equation.

$3 x = - 6 - 7$

Subtract $7$ from $- 6$ .

$3 x = - 13$

Divide each term in $3 x = - 13$ by $3$ and simplify.

Divide each term in $3 x = - 13$ by $3$ .

$\frac{3 x}{3} = \frac{- 13}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 x}{3} = \frac{- 13}{3}$

Divide $x$ by $1$ .

$x = \frac{- 13}{3}$

Simplify the right side.

Move the negative in front of the fraction.

$x = - \frac{13}{3}$

The complete solution is the result of both the positive and negative portions of the solution.

$x = - \frac{1}{3}, - \frac{13}{3}$

Solve Using the Square Root Property (3x+7)^2=36

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