Solve Using the Square Root Property (4y+15)^2=18

${(4 y + 15)}^{2} = 18$

Step 1

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

$4 y + 15 = \pm \sqrt{18}$

Step 2

Simplify $\pm \sqrt{18}$ .

Rewrite $18$ as $3^{2} \cdot 2$ .

Factor $9$ out of $18$ .

$4 y + 15 = \pm \sqrt{9 (2)}$

Rewrite $9$ as $3^{2}$ .

$4 y + 15 = \pm \sqrt{3^{2} \cdot 2}$

Pull terms out from under the radical.

$4 y + 15 = \pm 3 \sqrt{2}$

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.

$4 y + 15 = 3 \sqrt{2}$

Subtract $15$ from both sides of the equation.

$4 y = 3 \sqrt{2} - 15$

Divide each term in $4 y = 3 \sqrt{2} - 15$ by $4$ and simplify.

Divide each term in $4 y = 3 \sqrt{2} - 15$ by $4$ .

$\frac{4 y}{4} = \frac{3 \sqrt{2}}{4} + \frac{- 15}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 y}{4} = \frac{3 \sqrt{2}}{4} + \frac{- 15}{4}$

Divide $y$ by $1$ .

$y = \frac{3 \sqrt{2}}{4} + \frac{- 15}{4}$

Simplify the right side.

Move the negative in front of the fraction.

$y = \frac{3 \sqrt{2}}{4} - \frac{15}{4}$

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

$4 y + 15 = - 3 \sqrt{2}$

Subtract $15$ from both sides of the equation.

$4 y = - 3 \sqrt{2} - 15$

Divide each term in $4 y = - 3 \sqrt{2} - 15$ by $4$ and simplify.

Divide each term in $4 y = - 3 \sqrt{2} - 15$ by $4$ .

$\frac{4 y}{4} = \frac{- 3 \sqrt{2}}{4} + \frac{- 15}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 y}{4} = \frac{- 3 \sqrt{2}}{4} + \frac{- 15}{4}$

Divide $y$ by $1$ .

$y = \frac{- 3 \sqrt{2}}{4} + \frac{- 15}{4}$

Simplify the right side.

Simplify each term.

Move the negative in front of the fraction.

$y = - \frac{3 \sqrt{2}}{4} + \frac{- 15}{4}$

Move the negative in front of the fraction.

$y = - \frac{3 \sqrt{2}}{4} - \frac{15}{4}$

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

$y = \frac{3 \sqrt{2}}{4} - \frac{15}{4}, - \frac{3 \sqrt{2}}{4} - \frac{15}{4}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$y = \frac{3 \sqrt{2}}{4} - \frac{15}{4}, - \frac{3 \sqrt{2}}{4} - \frac{15}{4}$

Decimal Form:

$y = - 2.68933982 \dots, - 4.81066017 \dots$

Solve Using the Square Root Property (4y+15)^2=18

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