Solve 16x^2-8=0

$$16 x ^ { 2 } - 8 = 0$$

Solve for x

$$x=\frac{\sqrt{2}}{2}\approx 0.707106781$$

$$x=-\frac{\sqrt{2}}{2}\approx -0.707106781$$

Steps by Finding Square Root

Add 8 to both sides. Anything plus zero gives itself.

$$16x^{2}=8$$

Divide both sides by 16.

$$x^{2}=\frac{8}{16}$$

Reduce the fraction \frac{8}{16} to lowest terms by extracting and canceling out 8.

$$x^{2}=\frac{1}{2}$$

Take the square root of both sides of the equation.

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

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.

$$16x^{2}-8=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 16 for a, 0 for b, and -8 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 16\left(-8\right)}}{2\times 16}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 16\left(-8\right)}}{2\times 16}$$

Multiply -4 times 16.

$$x=\frac{0±\sqrt{-64\left(-8\right)}}{2\times 16}$$

Multiply -64 times -8.

$$x=\frac{0±\sqrt{512}}{2\times 16}$$

Take the square root of 512.

$$x=\frac{0±16\sqrt{2}}{2\times 16}$$

Multiply 2 times 16.

$$x=\frac{0±16\sqrt{2}}{32}$$

Now solve the equation x=\frac{0±16\sqrt{2}}{32} when ± is plus.

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

Now solve the equation x=\frac{0±16\sqrt{2}}{32} when ± is minus.

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

The equation is now solved.

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