Find the Roots (Zeros) g(x)=7x^2-567

$g (x) = 7 x^{2} - 567$

Step 1

Set $7 x^{2} - 567$ equal to $0$ .

$7 x^{2} - 567 = 0$

Step 2

Solve for $x$ .

Add $567$ to both sides of the equation.

$7 x^{2} = 567$

Divide each term in $7 x^{2} = 567$ by $7$ and simplify.

Divide each term in $7 x^{2} = 567$ by $7$ .

$\frac{7 x^{2}}{7} = \frac{567}{7}$

Simplify the left side.

Cancel the common factor of $7$ .

Cancel the common factor.

$\frac{7 x^{2}}{7} = \frac{567}{7}$

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

$x^{2} = \frac{567}{7}$

Simplify the right side.

Divide $567$ by $7$ .

$x^{2} = 81$

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

$x = \pm \sqrt{81}$

Simplify $\pm \sqrt{81}$ .

Rewrite $81$ as $9^{2}$ .

$x = \pm \sqrt{9^{2}}$

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

$x = \pm 9$

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.

$x = 9$

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

$x = - 9$

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

$x = 9, - 9$

Step 3