Find the Roots (Zeros) h(x)=1/5x^2-8

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

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

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

Solve for $x$ .

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

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

Add $8$ to both sides of the equation.

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

Multiply both sides of the equation by $5$ .

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

Simplify both sides of the equation.

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

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

Rewrite the expression.

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

Simplify the right side.

Multiply $5$ by $8$ .

$x^{2} = 40$

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

$x = \pm \sqrt{40}$

Simplify $\pm \sqrt{40}$ .

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

Factor $4$ out of $40$ .

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

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

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

Pull terms out from under the radical.

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

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

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

$x = 2 \sqrt{10}$

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

$x = - 2 \sqrt{10}$

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

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

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

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