Solve -9x^2=-486

$$- 9 x ^ { 2 } = - 486$$

Solve for x

$$x=3\sqrt{6}\approx 7.348469228$$

$$x=-3\sqrt{6}\approx -7.348469228$$

Steps by Finding Square Root

Divide both sides by -9.

$$x^{2}=\frac{-486}{-9}$$

Divide -486 by -9 to get 54.

$$x^{2}=54$$

Take the square root of both sides of the equation.

$$x=3\sqrt{6} x=-3\sqrt{6}$$

Steps Using the Quadratic Formula

Divide both sides by -9.

$$x^{2}=\frac{-486}{-9}$$

Divide -486 by -9 to get 54.

$$x^{2}=54$$

Subtract 54 from both sides.

$$x^{2}-54=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -54 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-54\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-54\right)}}{2}$$

Multiply -4 times -54.

$$x=\frac{0±\sqrt{216}}{2}$$

Take the square root of 216.

$$x=\frac{0±6\sqrt{6}}{2}$$

Now solve the equation x=\frac{0±6\sqrt{6}}{2} when ± is plus.

$$x=3\sqrt{6}$$

Now solve the equation x=\frac{0±6\sqrt{6}}{2} when ± is minus.

$$x=-3\sqrt{6}$$

The equation is now solved.

$$x=3\sqrt{6} x=-3\sqrt{6}$$