Solve 2x^2-2=64

$$2 x ^ { 2 } - 2 = 64$$

Solve for x

$$x=\sqrt{33}\approx 5.744562647$$

$$x=-\sqrt{33}\approx -5.744562647$$

Steps by Finding Square Root

Add 2 to both sides.

$$2x^{2}=64+2$$

Add 64 and 2 to get 66.

$$2x^{2}=66$$

Divide both sides by 2.

$$x^{2}=\frac{66}{2}$$

Divide 66 by 2 to get 33.

$$x^{2}=33$$

Take the square root of both sides of the equation.

$$x=\sqrt{33} x=-\sqrt{33}$$

Steps Using the Quadratic Formula

Subtract 64 from both sides.

$$2x^{2}-2-64=0$$

Subtract 64 from -2 to get -66.

$$2x^{2}-66=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 2 for a, 0 for b, and -66 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 2\left(-66\right)}}{2\times 2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 2\left(-66\right)}}{2\times 2}$$

Multiply -4 times 2.

$$x=\frac{0±\sqrt{-8\left(-66\right)}}{2\times 2}$$

Multiply -8 times -66.

$$x=\frac{0±\sqrt{528}}{2\times 2}$$

Take the square root of 528.

$$x=\frac{0±4\sqrt{33}}{2\times 2}$$

Multiply 2 times 2.

$$x=\frac{0±4\sqrt{33}}{4}$$

Now solve the equation x=\frac{0±4\sqrt{33}}{4} when ± is plus.

$$x=\sqrt{33}$$

Now solve the equation x=\frac{0±4\sqrt{33}}{4} when ± is minus.

$$x=-\sqrt{33}$$

The equation is now solved.

$$x=\sqrt{33} x=-\sqrt{33}$$