Algebra Examples

$f (x) = \frac{1}{5} x^{2} - 8$

Step 1

Set $\frac{1}{5} x^{2} - 8$ equal to $0$ .

$\frac{1}{5} x^{2} - 8 = 0$

Step 2

Solve for $x$ .

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Step 2.1

Combine $\frac{1}{5}$ and $x^{2}$ .

$\frac{x^{2}}{5} - 8 = 0$

Step 2.2

Add $8$ to both sides of the equation.

$\frac{x^{2}}{5} = 8$

Step 2.3

Multiply both sides of the equation by $5$ .

$5 \frac{x^{2}}{5} = 5 \cdot 8$

Step 2.4

Simplify both sides of the equation.

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Step 2.4.1

Simplify the left side.

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Step 2.4.1.1

Cancel the common factor of $5$ .

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Step 2.4.1.1.1

Cancel the common factor.

$5 \frac{x^{2}}{5} = 5 \cdot 8$

Step 2.4.1.1.2

Rewrite the expression.

$x^{2} = 5 \cdot 8$

Step 2.4.2

Simplify the right side.

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Step 2.4.2.1

Multiply $5$ by $8$ .

$x^{2} = 40$

Step 2.5

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

$x = \pm \sqrt{40}$

Step 2.6

Simplify $\pm \sqrt{40}$ .

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Step 2.6.1

Rewrite $40$ as $2^{2} \cdot 10$ .

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Step 2.6.1.1

Factor $4$ out of $40$ .

$x = \pm \sqrt{4 (10)}$

Step 2.6.1.2

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

$x = \pm \sqrt{2^{2} \cdot 10}$

Step 2.6.2

Pull terms out from under the radical.

$x = \pm 2 \sqrt{10}$

Step 2.7

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

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Step 2.7.1

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

$x = 2 \sqrt{10}$

Step 2.7.2

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

$x = - 2 \sqrt{10}$

Step 2.7.3

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

$x = 2 \sqrt{10}, - 2 \sqrt{10}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$x = 2 \sqrt{10}, - 2 \sqrt{10}$

Decimal Form:

$x = 6.32455532 \dots, - 6.32455532 \dots$

Step 4