Find the Roots (Zeros) -x^2-8=-33

$- x^{2} - 8 = - 33$

Step 1

Move all terms not containing $x$ to the right side of the equation.

Add $8$ to both sides of the equation.

$- x^{2} = - 33 + 8$

Add $- 33$ and $8$ .

$- x^{2} = - 25$

Step 2

Divide each term in $- x^{2} = - 25$ by $- 1$ and simplify.

Divide each term in $- x^{2} = - 25$ by $- 1$ .

$\frac{- x^{2}}{- 1} = \frac{- 25}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{x^{2}}{1} = \frac{- 25}{- 1}$

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

$x^{2} = \frac{- 25}{- 1}$

Simplify the right side.

Divide $- 25$ by $- 1$ .

$x^{2} = 25$

Step 3

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

$x = \pm \sqrt{25}$

Step 4

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.

$x = \pm 5$

Step 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 6