Algebra Examples

${(3 y + 9)}^{2} = 81$

Step 1

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

$3 y + 9 = \pm \sqrt{81}$

Step 2

Simplify $\pm \sqrt{81}$ .

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Step 2.1

Rewrite $81$ as $9^{2}$ .

$3 y + 9 = \pm \sqrt{9^{2}}$

Step 2.2

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

$3 y + 9 = \pm 9$

Step 3

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

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Step 3.1

First, use the positive value of the $\pm$ to find the first solution.

$3 y + 9 = 9$

Step 3.2

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

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Step 3.2.1

Subtract $9$ from both sides of the equation.

$3 y = 9 - 9$

Step 3.2.2

Subtract $9$ from $9$ .

$3 y = 0$

Step 3.3

Divide each term in $3 y = 0$ by $3$ and simplify.

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Step 3.3.1

Divide each term in $3 y = 0$ by $3$ .

$\frac{3 y}{3} = \frac{0}{3}$

Step 3.3.2

Simplify the left side.

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Step 3.3.2.1

Cancel the common factor of $3$ .

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Step 3.3.2.1.1

Cancel the common factor.

$\frac{3 y}{3} = \frac{0}{3}$

Step 3.3.2.1.2

Divide $y$ by $1$ .

$y = \frac{0}{3}$

Step 3.3.3

Simplify the right side.

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Step 3.3.3.1

Divide $0$ by $3$ .

$y = 0$

Step 3.4

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

$3 y + 9 = - 9$

Step 3.5

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

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Step 3.5.1

Subtract $9$ from both sides of the equation.

$3 y = - 9 - 9$

Step 3.5.2

Subtract $9$ from $- 9$ .

$3 y = - 18$

Step 3.6

Divide each term in $3 y = - 18$ by $3$ and simplify.

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Step 3.6.1

Divide each term in $3 y = - 18$ by $3$ .

$\frac{3 y}{3} = \frac{- 18}{3}$

Step 3.6.2

Simplify the left side.

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Step 3.6.2.1

Cancel the common factor of $3$ .

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Step 3.6.2.1.1

Cancel the common factor.

$\frac{3 y}{3} = \frac{- 18}{3}$

Step 3.6.2.1.2

Divide $y$ by $1$ .

$y = \frac{- 18}{3}$

Step 3.6.3

Simplify the right side.

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Step 3.6.3.1

Divide $- 18$ by $3$ .

$y = - 6$

Step 3.7

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

$y = 0, - 6$