Algebra Examples

$8 x^{2} - 18 = 0$

Step 1

Add $18$ to both sides of the equation.

$8 x^{2} = 18$

Step 2

Divide each term in $8 x^{2} = 18$ by $8$ and simplify.

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Step 2.1

Divide each term in $8 x^{2} = 18$ by $8$ .

$\frac{8 x^{2}}{8} = \frac{18}{8}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $8$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{8 x^{2}}{8} = \frac{18}{8}$

Step 2.2.1.2

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

$x^{2} = \frac{18}{8}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Cancel the common factor of $18$ and $8$ .

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Step 2.3.1.1

Factor $2$ out of $18$ .

$x^{2} = \frac{2 (9)}{8}$

Step 2.3.1.2

Cancel the common factors.

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Step 2.3.1.2.1

Factor $2$ out of $8$ .

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

Step 2.3.1.2.2

Cancel the common factor.

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

Step 2.3.1.2.3

Rewrite the expression.

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

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.

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