Solve Using the Square Root Property (4y+6)^2=36

${(4 y + 6)}^{2} = 36$

Step 1

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

$4 y + 6 = \pm \sqrt{36}$

Step 2

Simplify $\pm \sqrt{36}$ .

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

$4 y + 6 = \pm \sqrt{6^{2}}$

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

$4 y + 6 = \pm 6$

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.

$4 y + 6 = 6$

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

Subtract $6$ from both sides of the equation.

$4 y = 6 - 6$

Subtract $6$ from $6$ .

$4 y = 0$

Divide each term in $4 y = 0$ by $4$ and simplify.

Divide each term in $4 y = 0$ by $4$ .

$\frac{4 y}{4} = \frac{0}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 y}{4} = \frac{0}{4}$

Divide $y$ by $1$ .

$y = \frac{0}{4}$

Simplify the right side.

Divide $0$ by $4$ .

$y = 0$

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

$4 y + 6 = - 6$

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

Subtract $6$ from both sides of the equation.

$4 y = - 6 - 6$

Subtract $6$ from $- 6$ .

$4 y = - 12$

Divide each term in $4 y = - 12$ by $4$ and simplify.

Divide each term in $4 y = - 12$ by $4$ .

$\frac{4 y}{4} = \frac{- 12}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 y}{4} = \frac{- 12}{4}$

Divide $y$ by $1$ .

$y = \frac{- 12}{4}$

Simplify the right side.

Divide $- 12$ by $4$ .

$y = - 3$

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

$y = 0, - 3$

Solve Using the Square Root Property (4y+6)^2=36

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