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

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

Step 1

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

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

Step 2

Simplify $\pm \sqrt{4}$ .

Rewrite $4$ as $2^{2}$ .

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

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

$4 y + 2 = \pm 2$

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.

$4 y + 2 = 2$

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

Subtract $2$ from both sides of the equation.

$4 y = 2 - 2$

Subtract $2$ from $2$ .

$4 y = 0$

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.

$4 y + 2 = - 2$

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

Subtract $2$ from both sides of the equation.

$4 y = - 2 - 2$

Subtract $2$ from $- 2$ .

$4 y = - 4$

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

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

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

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

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

Divide $y$ by $1$ .

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

Simplify the right side.

Divide $- 4$ by $4$ .

$y = - 1$

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

$y = 0, - 1$

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

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