Solve z^2=0.64

$$z ^ { 2 } = 0.64$$

Solve for z

$$z=0.8$$

$$z=-0.8$$

Steps Using Difference of Squares

Subtract 0.64 from both sides.

$$z^{2}-0.64=0$$

Consider z^{2}-0.64. Rewrite z^{2}-0.64 as z^{2}-\left(\frac{4}{5}\right)^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(z-\frac{4}{5}\right)\left(z+\frac{4}{5}\right)=0$$

To find equation solutions, solve z-\frac{4}{5}=0 and z+\frac{4}{5}=0.

$$z=\frac{4}{5} z=-\frac{4}{5}$$

Steps by Finding Square Root

Take the square root of both sides of the equation.

$$z=\frac{4}{5} z=-\frac{4}{5}$$

Steps Using the Quadratic Formula

Subtract 0.64 from both sides.

$$z^{2}-0.64=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -0.64 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$z=\frac{0±\sqrt{0^{2}-4\left(-0.64\right)}}{2}$$

Square 0.

$$z=\frac{0±\sqrt{-4\left(-0.64\right)}}{2}$$

Multiply -4 times -0.64.

$$z=\frac{0±\sqrt{2.56}}{2}$$

Take the square root of 2.56.

$$z=\frac{0±\frac{8}{5}}{2}$$

Now solve the equation z=\frac{0±\frac{8}{5}}{2} when ± is plus.

$$z=\frac{4}{5}$$

Now solve the equation z=\frac{0±\frac{8}{5}}{2} when ± is minus.

$$z=-\frac{4}{5}$$

The equation is now solved.

$$z=\frac{4}{5} z=-\frac{4}{5}$$