Algebra Examples

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

Step 1

Add $9$ to both sides of the equation.

$4 x^{2} = 9$

Step 2

Divide each term in $4 x^{2} = 9$ by $4$ and simplify.

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Step 2.1

Divide each term in $4 x^{2} = 9$ by $4$ .

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

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $4$ .

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Step 2.2.1.1

Cancel the common factor.

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

Step 2.2.1.2

Divide $x^{2}$ by $1$ .

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

Step 3

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

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

Step 4

Simplify $\pm \sqrt{\frac{9}{4}}$ .

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Step 4.1

Rewrite $\sqrt{\frac{9}{4}}$ as $\frac{\sqrt{9}}{\sqrt{4}}$ .

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

Step 4.2

Simplify the numerator.

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Step 4.2.1

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

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

Step 4.2.2

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

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

Step 4.3

Simplify the denominator.

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Step 4.3.1

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

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

Step 4.3.2

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

$x = \pm \frac{3}{2}$

Step 5

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

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Step 5.1

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

$x = \frac{3}{2}$

Step 5.2

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

$x = - \frac{3}{2}$

Step 5.3

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

$x = \frac{3}{2}, - \frac{3}{2}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$x = \frac{3}{2}, - \frac{3}{2}$

Decimal Form:

$x = 1.5, - 1.5$

Mixed Number Form:

$x = 1 \frac{1}{2}, - 1 \frac{1}{2}$