Solve Using the Square Root Property (5y+4)^2+121=0

${(5 y + 4)}^{2} + 121 = 0$

Step 1

Subtract $121$ from both sides of the equation.

${(5 y + 4)}^{2} = - 121$

Step 2

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

$5 y + 4 = \pm \sqrt{- 121}$

Step 3

Simplify $\pm \sqrt{- 121}$ .

Rewrite $- 121$ as $- 1 (121)$ .

$5 y + 4 = \pm \sqrt{- 1 (121)}$

Rewrite $\sqrt{- 1 (121)}$ as $\sqrt{- 1} \cdot \sqrt{121}$ .

$5 y + 4 = \pm \sqrt{- 1} \cdot \sqrt{121}$

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

$5 y + 4 = \pm i \cdot \sqrt{121}$

Rewrite $121$ as $11^{2}$ .

$5 y + 4 = \pm i \cdot \sqrt{11^{2}}$

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

$5 y + 4 = \pm i \cdot 11$

Move $11$ to the left of $i$ .

$5 y + 4 = \pm 11 i$

Step 4

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.

$5 y + 4 = 11 i$

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

Subtract $4$ from both sides of the equation.

$5 y = 11 i - 4$

Reorder $11 i$ and $- 4$ .

$5 y = - 4 + 11 i$

Divide each term in $5 y = - 4 + 11 i$ by $5$ and simplify.

Divide each term in $5 y = - 4 + 11 i$ by $5$ .

$\frac{5 y}{5} = \frac{- 4}{5} + \frac{11 i}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 y}{5} = \frac{- 4}{5} + \frac{11 i}{5}$

Divide $y$ by $1$ .

$y = \frac{- 4}{5} + \frac{11 i}{5}$

Simplify the right side.

Move the negative in front of the fraction.

$y = - \frac{4}{5} + \frac{11 i}{5}$

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

$5 y + 4 = - 11 i$

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

Subtract $4$ from both sides of the equation.

$5 y = - 11 i - 4$

Reorder $- 11 i$ and $- 4$ .

$5 y = - 4 - 11 i$

Divide each term in $5 y = - 4 - 11 i$ by $5$ and simplify.

Divide each term in $5 y = - 4 - 11 i$ by $5$ .

$\frac{5 y}{5} = \frac{- 4}{5} + \frac{- 11 i}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 y}{5} = \frac{- 4}{5} + \frac{- 11 i}{5}$

Divide $y$ by $1$ .

$y = \frac{- 4}{5} + \frac{- 11 i}{5}$

Simplify the right side.

Simplify each term.

Move the negative in front of the fraction.

$y = - \frac{4}{5} + \frac{- 11 i}{5}$

Move the negative in front of the fraction.

$y = - \frac{4}{5} - \frac{11 i}{5}$

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

$y = - \frac{4}{5} + \frac{11 i}{5}, - \frac{4}{5} - \frac{11 i}{5}$

Solve Using the Square Root Property (5y+4)^2+121=0

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