Solve z^2=64

$$z ^ { 2 } = 64$$

Solve for z

$$z=8$$

$$z=-8$$

Steps Using Difference of Squares

Subtract 64 from both sides.

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

Consider z^{2}-64. Rewrite z^{2}-64 as z^{2}-8^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(z-8\right)\left(z+8\right)=0$$

To find equation solutions, solve z-8=0 and z+8=0.

$$z=8 z=-8$$

Steps by Finding Square Root

Take the square root of both sides of the equation.

$$z=8 z=-8$$

Steps Using the Quadratic Formula

Subtract 64 from both sides.

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

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -64 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

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

Square 0.

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

Multiply -4 times -64.

$$z=\frac{0±\sqrt{256}}{2}$$

Take the square root of 256.

$$z=\frac{0±16}{2}$$

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

$$z=8$$

Now solve the equation z=\frac{0±16}{2} when ± is minus. Divide -16 by 2.

$$z=-8$$

The equation is now solved.

$$z=8 z=-8$$