Pre-Algebra Examples

$\frac{1}{4} x^{2} - \frac{4}{9} = 0$

Step 1

Combine $\frac{1}{4}$ and $x^{2}$ .

$\frac{x^{2}}{4} - \frac{4}{9} = 0$

Step 2

Add $\frac{4}{9}$ to both sides of the equation.

$\frac{x^{2}}{4} = \frac{4}{9}$

Step 3

Multiply both sides of the equation by $4$ .

$4 \frac{x^{2}}{4} = 4 (\frac{4}{9})$

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

Cancel the common factor of $4$ .

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Step 4.1.1.1

Cancel the common factor.

$4 \frac{x^{2}}{4} = 4 (\frac{4}{9})$

Step 4.1.1.2

Rewrite the expression.

$x^{2} = 4 (\frac{4}{9})$

Step 4.2

Simplify the right side.

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Step 4.2.1

Multiply $4 (\frac{4}{9})$ .

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Step 4.2.1.1

Combine $4$ and $\frac{4}{9}$ .

$x^{2} = \frac{4 \cdot 4}{9}$

Step 4.2.1.2

Multiply $4$ by $4$ .

$x^{2} = \frac{16}{9}$

Step 5

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

$x = \pm \sqrt{\frac{16}{9}}$

Step 6

Simplify $\pm \sqrt{\frac{16}{9}}$ .

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Step 6.1

Rewrite $\sqrt{\frac{16}{9}}$ as $\frac{\sqrt{16}}{\sqrt{9}}$ .

$x = \pm \frac{\sqrt{16}}{\sqrt{9}}$

Step 6.2

Simplify the numerator.

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Step 6.2.1

Rewrite $16$ as $4^{2}$ .

$x = \pm \frac{\sqrt{4^{2}}}{\sqrt{9}}$

Step 6.2.2

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

$x = \pm \frac{4}{\sqrt{9}}$

Step 6.3

Simplify the denominator.

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Step 6.3.1

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

$x = \pm \frac{4}{\sqrt{3^{2}}}$

Step 6.3.2

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

$x = \pm \frac{4}{3}$

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.

$x = \frac{4}{3}$

Step 7.2

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

$x = - \frac{4}{3}$

Step 7.3

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

$x = \frac{4}{3}, - \frac{4}{3}$