Find the Roots (Zeros) f(x)=-2(x^2-4)

$f (x) = - 2 (x^{2} - 4)$

Step 1

Set $- 2 (x^{2} - 4)$ equal to $0$ .

$- 2 (x^{2} - 4) = 0$

Step 2

Solve for $x$ .

Divide each term in $- 2 (x^{2} - 4) = 0$ by $- 2$ and simplify.

Divide each term in $- 2 (x^{2} - 4) = 0$ by $- 2$ .

$\frac{- 2 (x^{2} - 4)}{- 2} = \frac{0}{- 2}$

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

$\frac{- 2 (x^{2} - 4)}{- 2} = \frac{0}{- 2}$

Divide $x^{2} - 4$ by $1$ .

$x^{2} - 4 = \frac{0}{- 2}$

Simplify the right side.

Divide $0$ by $- 2$ .

$x^{2} - 4 = 0$

Add $4$ to both sides of the equation.

$x^{2} = 4$

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

$x = \pm \sqrt{4}$

Simplify $\pm \sqrt{4}$ .

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

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

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

$x = \pm 2$

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.

$x = 2$

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

$x = - 2$

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

$x = 2, - 2$

Step 3