Find the Roots (Zeros) f(x)=8x^2-800

$f (x) = 8 x^{2} - 800$

Step 1

Set $8 x^{2} - 800$ equal to $0$ .

$8 x^{2} - 800 = 0$

Step 2

Solve for $x$ .

Add $800$ to both sides of the equation.

$8 x^{2} = 800$

Divide each term in $8 x^{2} = 800$ by $8$ and simplify.

Divide each term in $8 x^{2} = 800$ by $8$ .

$\frac{8 x^{2}}{8} = \frac{800}{8}$

Simplify the left side.

Cancel the common factor of $8$ .

Cancel the common factor.

$\frac{8 x^{2}}{8} = \frac{800}{8}$

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

$x^{2} = \frac{800}{8}$

Simplify the right side.

Divide $800$ by $8$ .

$x^{2} = 100$

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

$x = \pm \sqrt{100}$

Simplify $\pm \sqrt{100}$ .

Rewrite $100$ as $10^{2}$ .

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

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

$x = \pm 10$

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.

$x = 10$

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

$x = - 10$

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

$x = 10, - 10$

Step 3