Solve 2x^2=81

$$2 x ^ { 2 } = 81$$

Solve for x

$$x = \frac{9 \sqrt{2}}{2} \approx 6.363961031$$

$$x = -\frac{9 \sqrt{2}}{2} \approx -6.363961031$$

Steps by Finding Square Root

Divide both sides by 2.

$$x^{2}=\frac{81}{2}$$

Take the square root of both sides of the equation.

$$x=\frac{9\sqrt{2}}{2} x=-\frac{9\sqrt{2}}{2}$$

Steps Using the Quadratic Formula

Divide both sides by 2.

$$x^{2}=\frac{81}{2}$$

Subtract \frac{81}{2} from both sides.

$$x^{2}-\frac{81}{2}=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -\frac{81}{2} for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-\frac{81}{2}\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-\frac{81}{2}\right)}}{2}$$

Multiply -4 times -\frac{81}{2}.

$$x=\frac{0±\sqrt{162}}{2}$$

Take the square root of 162.

$$x=\frac{0±9\sqrt{2}}{2}$$

Now solve the equation x=\frac{0±9\sqrt{2}}{2} when ± is plus.

$$x=\frac{9\sqrt{2}}{2}$$

Now solve the equation x=\frac{0±9\sqrt{2}}{2} when ± is minus.

$$x=-\frac{9\sqrt{2}}{2}$$

The equation is now solved.

$$x=\frac{9\sqrt{2}}{2} x=-\frac{9\sqrt{2}}{2}$$