Solve Using the Square Root Property (11y-7)^2+144=0

${(11 y - 7)}^{2} + 144 = 0$

Step 1

Subtract $144$ from both sides of the equation.

${(11 y - 7)}^{2} = - 144$

Step 2

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

$11 y - 7 = \pm \sqrt{- 144}$

Step 3

Simplify $\pm \sqrt{- 144}$ .

Rewrite $- 144$ as $- 1 (144)$ .

$11 y - 7 = \pm \sqrt{- 1 (144)}$

Rewrite $\sqrt{- 1 (144)}$ as $\sqrt{- 1} \cdot \sqrt{144}$ .

$11 y - 7 = \pm \sqrt{- 1} \cdot \sqrt{144}$

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

$11 y - 7 = \pm i \cdot \sqrt{144}$

Rewrite $144$ as $12^{2}$ .

$11 y - 7 = \pm i \cdot \sqrt{12^{2}}$

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

$11 y - 7 = \pm i \cdot 12$

Move $12$ to the left of $i$ .

$11 y - 7 = \pm 12 i$

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.

$11 y - 7 = 12 i$

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

Add $7$ to both sides of the equation.

$11 y = 12 i + 7$

Reorder $12 i$ and $7$ .

$11 y = 7 + 12 i$

Divide each term in $11 y = 7 + 12 i$ by $11$ and simplify.

Divide each term in $11 y = 7 + 12 i$ by $11$ .

$\frac{11 y}{11} = \frac{7}{11} + \frac{12 i}{11}$

Simplify the left side.

Cancel the common factor of $11$ .

Cancel the common factor.

$\frac{11 y}{11} = \frac{7}{11} + \frac{12 i}{11}$

Divide $y$ by $1$ .

$y = \frac{7}{11} + \frac{12 i}{11}$

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

$11 y - 7 = - 12 i$

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

Add $7$ to both sides of the equation.

$11 y = - 12 i + 7$

Reorder $- 12 i$ and $7$ .

$11 y = 7 - 12 i$

Divide each term in $11 y = 7 - 12 i$ by $11$ and simplify.

Divide each term in $11 y = 7 - 12 i$ by $11$ .

$\frac{11 y}{11} = \frac{7}{11} + \frac{- 12 i}{11}$

Simplify the left side.

Cancel the common factor of $11$ .

Cancel the common factor.

$\frac{11 y}{11} = \frac{7}{11} + \frac{- 12 i}{11}$

Divide $y$ by $1$ .

$y = \frac{7}{11} + \frac{- 12 i}{11}$

Simplify the right side.

Move the negative in front of the fraction.

$y = \frac{7}{11} - \frac{12 i}{11}$

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

$y = \frac{7}{11} + \frac{12 i}{11}, \frac{7}{11} - \frac{12 i}{11}$

Solve Using the Square Root Property (11y-7)^2+144=0

Related Questions

Support LCMGCF.com by disabling your adblocker.