Find the Roots (Zeros) h(x)=-5x^2+180

$h (x) = - 5 x^{2} + 180$

Step 1

Set $- 5 x^{2} + 180$ equal to $0$ .

$- 5 x^{2} + 180 = 0$

Step 2

Solve for $x$ .

Subtract $180$ from both sides of the equation.

$- 5 x^{2} = - 180$

Divide each term in $- 5 x^{2} = - 180$ by $- 5$ and simplify.

Divide each term in $- 5 x^{2} = - 180$ by $- 5$ .

$\frac{- 5 x^{2}}{- 5} = \frac{- 180}{- 5}$

Simplify the left side.

Cancel the common factor of $- 5$ .

Cancel the common factor.

$\frac{- 5 x^{2}}{- 5} = \frac{- 180}{- 5}$

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

$x^{2} = \frac{- 180}{- 5}$

Simplify the right side.

Divide $- 180$ by $- 5$ .

$x^{2} = 36$

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

$x = \pm \sqrt{36}$

Simplify $\pm \sqrt{36}$ .

Rewrite $36$ as $6^{2}$ .

$x = \pm \sqrt{6^{2}}$

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

$x = \pm 6$

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.

$x = 6$

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

$x = - 6$

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

$x = 6, - 6$

Step 3