Solve z^2=225

$$z ^ { 2 } = 225$$

Solve for z

$$z=15$$

$$z=-15$$

Steps Using Difference of Squares

Subtract 225 from both sides.

$$z^{2}-225=0$$

Consider z^{2}-225. Rewrite z^{2}-225 as z^{2}-15^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(z-15\right)\left(z+15\right)=0$$

To find equation solutions, solve z-15=0 and z+15=0.

$$z=15 z=-15$$

Steps by Finding Square Root

Take the square root of both sides of the equation.

$$z=15 z=-15$$

Steps Using the Quadratic Formula

Subtract 225 from both sides.

$$z^{2}-225=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -225 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$z=\frac{0±\sqrt{0^{2}-4\left(-225\right)}}{2}$$

Square 0.

$$z=\frac{0±\sqrt{-4\left(-225\right)}}{2}$$

Multiply -4 times -225.

$$z=\frac{0±\sqrt{900}}{2}$$

Take the square root of 900.

$$z=\frac{0±30}{2}$$

Now solve the equation z=\frac{0±30}{2} when ± is plus. Divide 30 by 2.

$$z=15$$

Now solve the equation z=\frac{0±30}{2} when ± is minus. Divide -30 by 2.

$$z=-15$$

The equation is now solved.

$$z=15 z=-15$$