Solve -3x^2=-213

$$- 3 x ^ { 2 } = - 213$$

Solve for x

$$x=\sqrt{71}\approx 8.426149773$$

$$x=-\sqrt{71}\approx -8.426149773$$

Steps by Finding Square Root

Divide both sides by -3.

$$x^{2}=\frac{-213}{-3}$$

Divide -213 by -3 to get 71.

$$x^{2}=71$$

Take the square root of both sides of the equation.

$$x=\sqrt{71} x=-\sqrt{71}$$

Steps Using the Quadratic Formula

Divide both sides by -3.

$$x^{2}=\frac{-213}{-3}$$

Divide -213 by -3 to get 71.

$$x^{2}=71$$

Subtract 71 from both sides.

$$x^{2}-71=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -71 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-71\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-71\right)}}{2}$$

Multiply -4 times -71.

$$x=\frac{0±\sqrt{284}}{2}$$

Take the square root of 284.

$$x=\frac{0±2\sqrt{71}}{2}$$

Now solve the equation x=\frac{0±2\sqrt{71}}{2} when ± is plus.

$$x=\sqrt{71}$$

Now solve the equation x=\frac{0±2\sqrt{71}}{2} when ± is minus.

$$x=-\sqrt{71}$$

The equation is now solved.

$$x=\sqrt{71} x=-\sqrt{71}$$