Pre-Algebra Examples

$\frac{2}{3} \cdot {(h + 8)}^{2} - 66 = 0$

Step 1

Add $66$ to both sides of the equation.

$\frac{2}{3} \cdot {(h + 8)}^{2} = 66$

Step 2

Combine $\frac{2}{3}$ and ${(h + 8)}^{2}$ .

$\frac{2 {(h + 8)}^{2}}{3} = 66$

Step 3

Multiply both sides of the equation by $\frac{3}{2}$ .

$\frac{3}{2} \cdot \frac{2 {(h + 8)}^{2}}{3} = \frac{3}{2} \cdot 66$

Step 4

Simplify both sides of the equation.

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Step 4.1

Simplify the left side.

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Step 4.1.1

Simplify $\frac{3}{2} \cdot \frac{2 {(h + 8)}^{2}}{3}$ .

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Step 4.1.1.1

Combine.

$\frac{3 (2 {(h + 8)}^{2})}{2 \cdot 3} = \frac{3}{2} \cdot 66$

Step 4.1.1.2

Cancel the common factor of $3$ .

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Step 4.1.1.2.1

Cancel the common factor.

$\frac{3 (2 {(h + 8)}^{2})}{2 \cdot 3} = \frac{3}{2} \cdot 66$

Step 4.1.1.2.2

Rewrite the expression.

$\frac{2 {(h + 8)}^{2}}{2} = \frac{3}{2} \cdot 66$

Step 4.1.1.3

Cancel the common factor of $2$ .

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Step 4.1.1.3.1

Cancel the common factor.

$\frac{2 {(h + 8)}^{2}}{2} = \frac{3}{2} \cdot 66$

Step 4.1.1.3.2

Divide ${(h + 8)}^{2}$ by $1$ .

${(h + 8)}^{2} = \frac{3}{2} \cdot 66$

Step 4.2

Simplify the right side.

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Step 4.2.1

Simplify $\frac{3}{2} \cdot 66$ .

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Step 4.2.1.1

Cancel the common factor of $2$ .

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Step 4.2.1.1.1

Factor $2$ out of $66$ .

${(h + 8)}^{2} = \frac{3}{2} \cdot (2 (33))$

Step 4.2.1.1.2

Cancel the common factor.

${(h + 8)}^{2} = \frac{3}{2} \cdot (2 \cdot 33)$

Step 4.2.1.1.3

Rewrite the expression.

${(h + 8)}^{2} = 3 \cdot 33$

Step 4.2.1.2

Multiply $3$ by $33$ .

${(h + 8)}^{2} = 99$

Step 5

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

$h + 8 = \pm \sqrt{99}$

Step 6

Simplify $\pm \sqrt{99}$ .

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Step 6.1

Rewrite $99$ as $3^{2} \cdot 11$ .

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Step 6.1.1

Factor $9$ out of $99$ .

$h + 8 = \pm \sqrt{9 (11)}$

Step 6.1.2

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

$h + 8 = \pm \sqrt{3^{2} \cdot 11}$

Step 6.2

Pull terms out from under the radical.

$h + 8 = \pm 3 \sqrt{11}$

Step 7

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

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Step 7.1

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

$h + 8 = 3 \sqrt{11}$

Step 7.2

Subtract $8$ from both sides of the equation.

$h = 3 \sqrt{11} - 8$

Step 7.3

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

$h + 8 = - 3 \sqrt{11}$

Step 7.4

Subtract $8$ from both sides of the equation.

$h = - 3 \sqrt{11} - 8$

Step 7.5

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

$h = 3 \sqrt{11} - 8, - 3 \sqrt{11} - 8$

Step 8

The result can be shown in multiple forms.

Exact Form:

$h = 3 \sqrt{11} - 8, - 3 \sqrt{11} - 8$

Decimal Form:

$h = 1.94987437 \dots, - 17.94987437 \dots$