Find the Roots (Zeros) f(x)=-3x^2+75

$f (x) = - 3 x^{2} + 75$

Step 1

Set $- 3 x^{2} + 75$ equal to $0$ .

$- 3 x^{2} + 75 = 0$

Step 2

Solve for $x$ .

Subtract $75$ from both sides of the equation.

$- 3 x^{2} = - 75$

Divide each term in $- 3 x^{2} = - 75$ by $- 3$ and simplify.

Divide each term in $- 3 x^{2} = - 75$ by $- 3$ .

$\frac{- 3 x^{2}}{- 3} = \frac{- 75}{- 3}$

Simplify the left side.

Cancel the common factor of $- 3$ .

Cancel the common factor.

$\frac{- 3 x^{2}}{- 3} = \frac{- 75}{- 3}$

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

$x^{2} = \frac{- 75}{- 3}$

Simplify the right side.

Divide $- 75$ by $- 3$ .

$x^{2} = 25$

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

$x = \pm \sqrt{25}$

Simplify $\pm \sqrt{25}$ .

Rewrite $25$ as $5^{2}$ .

$x = \pm \sqrt{5^{2}}$

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

$x = \pm 5$

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.

$x = 5$

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

$x = - 5$

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

$x = 5, - 5$

Step 3