Find the Roots (Zeros) y=9x^2-36

$y = 9 x^{2} - 36$

Step 1

Set $9 x^{2} - 36$ equal to $0$ .

$9 x^{2} - 36 = 0$

Step 2

Solve for $x$ .

Add $36$ to both sides of the equation.

$9 x^{2} = 36$

Divide each term in $9 x^{2} = 36$ by $9$ and simplify.

Divide each term in $9 x^{2} = 36$ by $9$ .

$\frac{9 x^{2}}{9} = \frac{36}{9}$

Simplify the left side.

Cancel the common factor of $9$ .

Cancel the common factor.

$\frac{9 x^{2}}{9} = \frac{36}{9}$

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

$x^{2} = \frac{36}{9}$

Simplify the right side.

Divide $36$ by $9$ .

$x^{2} = 4$

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