Solve z^2-16=0

$$z ^ { 2 } - 16 = 0$$

Solve for z

$$z=4$$

$$z=-4$$

Steps Using Difference of Squares

Consider z^{2}-16. Rewrite z^{2}-16 as z^{2}-4^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(z-4\right)\left(z+4\right)=0$$

To find equation solutions, solve z-4=0 and z+4=0.

$$z=4 z=-4$$

Steps by Finding Square Root

Add 16 to both sides. Anything plus zero gives itself.

$$z^{2}=16$$

Take the square root of both sides of the equation.

$$z=4 z=-4$$

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.

$$z^{2}-16=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -16 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

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

Square 0.

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

Multiply -4 times -16.

$$z=\frac{0±\sqrt{64}}{2}$$

Take the square root of 64.

$$z=\frac{0±8}{2}$$

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

$$z=4$$

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

$$z=-4$$

The equation is now solved.

$$z=4 z=-4$$