Solve Using the Square Root Property -3x^2+297=0

$- 3 x^{2} + 297 = 0$

Step 1

Subtract $297$ from both sides of the equation.

$- 3 x^{2} = - 297$

Step 2

Divide each term in $- 3 x^{2} = - 297$ by $- 3$ and simplify.

Divide each term in $- 3 x^{2} = - 297$ by $- 3$ .

$\frac{- 3 x^{2}}{- 3} = \frac{- 297}{- 3}$

Simplify the left side.

Cancel the common factor of $- 3$ .

Cancel the common factor.

$\frac{- 3 x^{2}}{- 3} = \frac{- 297}{- 3}$

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

$x^{2} = \frac{- 297}{- 3}$

Simplify the right side.

Divide $- 297$ by $- 3$ .

$x^{2} = 99$

Step 3

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

$x = \pm \sqrt{99}$

Step 4

Simplify $\pm \sqrt{99}$ .

Rewrite $99$ as $3^{2} \cdot 11$ .

Factor $9$ out of $99$ .

$x = \pm \sqrt{9 (11)}$

Rewrite $9$ as $3^{2}$ .

$x = \pm \sqrt{3^{2} \cdot 11}$

Pull terms out from under the radical.

$x = \pm 3 \sqrt{11}$

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.

$x = 3 \sqrt{11}$

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

$x = - 3 \sqrt{11}$

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

$x = 3 \sqrt{11}, - 3 \sqrt{11}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$x = 3 \sqrt{11}, - 3 \sqrt{11}$

Decimal Form:

$x = 9.94987437 \dots, - 9.94987437 \dots$