Solve Using the Square Root Property 5-6y^2=113

$5 - 6 y^{2} = 113$

Step 1

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

Subtract $5$ from both sides of the equation.

$- 6 y^{2} = 113 - 5$

Subtract $5$ from $113$ .

$- 6 y^{2} = 108$

Step 2

Divide each term in $- 6 y^{2} = 108$ by $- 6$ and simplify.

Divide each term in $- 6 y^{2} = 108$ by $- 6$ .

$\frac{- 6 y^{2}}{- 6} = \frac{108}{- 6}$

Simplify the left side.

Cancel the common factor of $- 6$ .

Cancel the common factor.

$\frac{- 6 y^{2}}{- 6} = \frac{108}{- 6}$

Divide $y^{2}$ by $1$ .

$y^{2} = \frac{108}{- 6}$

Simplify the right side.

Divide $108$ by $- 6$ .

$y^{2} = - 18$

Step 3

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

$y = \pm \sqrt{- 18}$

Step 4

Simplify $\pm \sqrt{- 18}$ .

Rewrite $- 18$ as $- 1 (18)$ .

$y = \pm \sqrt{- 1 (18)}$

Rewrite $\sqrt{- 1 (18)}$ as $\sqrt{- 1} \cdot \sqrt{18}$ .

$y = \pm \sqrt{- 1} \cdot \sqrt{18}$

Rewrite $\sqrt{- 1}$ as $i$ .

$y = \pm i \cdot \sqrt{18}$

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

Factor $9$ out of $18$ .

$y = \pm i \cdot \sqrt{9 (2)}$

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

$y = \pm i \cdot \sqrt{3^{2} \cdot 2}$

Pull terms out from under the radical.

$y = \pm i \cdot (3 \sqrt{2})$

Move $3$ to the left of $i$ .

$y = \pm 3 i \sqrt{2}$

Step 5

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.

$y = 3 i \sqrt{2}$

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

$y = - 3 i \sqrt{2}$

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

$y = 3 i \sqrt{2}, - 3 i \sqrt{2}$

Solve Using the Square Root Property 5-6y^2=113

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