Solve 8z^2-4=0

$$8 z ^ { 2 } - 4 = 0$$

Solve for z

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

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

Steps by Finding Square Root

Add 4 to both sides. Anything plus zero gives itself.

$$8z^{2}=4$$

Divide both sides by 8.

$$z^{2}=\frac{4}{8}$$

Reduce the fraction \frac{4}{8} to lowest terms by extracting and canceling out 4.

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

Take the square root of both sides of the equation.

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

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.

$$8z^{2}-4=0$$

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

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

Square 0.

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

Multiply -4 times 8.

$$z=\frac{0±\sqrt{-32\left(-4\right)}}{2\times 8}$$

Multiply -32 times -4.

$$z=\frac{0±\sqrt{128}}{2\times 8}$$

Take the square root of 128.

$$z=\frac{0±8\sqrt{2}}{2\times 8}$$

Multiply 2 times 8.

$$z=\frac{0±8\sqrt{2}}{16}$$

Now solve the equation z=\frac{0±8\sqrt{2}}{16} when ± is plus.

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

Now solve the equation z=\frac{0±8\sqrt{2}}{16} when ± is minus.

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

The equation is now solved.

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