Solve 2x^2-64=0

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

Solve for x

$$x=4\sqrt{2}\approx 5.656854249$$

$$x=-4\sqrt{2}\approx -5.656854249$$

Steps by Finding Square Root

Add 64 to both sides. Anything plus zero gives itself.

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

Divide both sides by 2.

$$x^{2}=\frac{64}{2}$$

Divide 64 by 2 to get 32.

$$x^{2}=32$$

Take the square root of both sides of the equation.

$$x=4\sqrt{2} x=-4\sqrt{2}$$

Steps Using the Quadratic Formula

Quadratic equations like this one, with an x^{2} term but no x term, can still be solved using the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}, once they are put in standard form: ax^{2}+bx+c=0.

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

This equation is in standard form: ax^{2}+bx+c=0. Substitute 2 for a, 0 for b, and -64 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 2\left(-64\right)}}{2\times 2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 2\left(-64\right)}}{2\times 2}$$

Multiply -4 times 2.

$$x=\frac{0±\sqrt{-8\left(-64\right)}}{2\times 2}$$

Multiply -8 times -64.

$$x=\frac{0±\sqrt{512}}{2\times 2}$$

Take the square root of 512.

$$x=\frac{0±16\sqrt{2}}{2\times 2}$$

Multiply 2 times 2.

$$x=\frac{0±16\sqrt{2}}{4}$$

Now solve the equation x=\frac{0±16\sqrt{2}}{4} when ± is plus.

$$x=4\sqrt{2}$$

Now solve the equation x=\frac{0±16\sqrt{2}}{4} when ± is minus.

$$x=-4\sqrt{2}$$

The equation is now solved.

$$x=4\sqrt{2} x=-4\sqrt{2}$$