Solve Using the Square Root Property -6x^2=-414

$- 6 x^{2} = - 414$

Step 1

Divide each term in $- 6 x^{2} = - 414$ by $- 6$ and simplify.

Divide each term in $- 6 x^{2} = - 414$ by $- 6$ .

$\frac{- 6 x^{2}}{- 6} = \frac{- 414}{- 6}$

Simplify the left side.

Cancel the common factor of $- 6$ .

Cancel the common factor.

$\frac{- 6 x^{2}}{- 6} = \frac{- 414}{- 6}$

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

$x^{2} = \frac{- 414}{- 6}$

Simplify the right side.

Divide $- 414$ by $- 6$ .

$x^{2} = 69$

Step 2

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

$x = \pm \sqrt{69}$

Step 3

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.

$x = \sqrt{69}$

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

$x = - \sqrt{69}$

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

$x = \sqrt{69}, - \sqrt{69}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \sqrt{69}, - \sqrt{69}$

Decimal Form:

$x = 8.30662386 \dots, - 8.30662386 \dots$