Solve 16=(z-3)(z+3)

$$16 = ( z - 3 ) ( z + 3 )$$

Solve for z

$$z=5$$

$$z=-5$$

Steps by Finding Square Root

Consider \left(z-3\right)\left(z+3\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}. Square 3.

$$16=z^{2}-9$$

Swap sides so that all variable terms are on the left hand side.

$$z^{2}-9=16$$

Add 9 to both sides.

$$z^{2}=16+9$$

Add 16 and 9 to get 25.

$$z^{2}=25$$

Take the square root of both sides of the equation.

$$z=5 z=-5$$

Steps Using the Quadratic Formula

Consider \left(z-3\right)\left(z+3\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}. Square 3.

$$16=z^{2}-9$$

Swap sides so that all variable terms are on the left hand side.

$$z^{2}-9=16$$

Subtract 16 from both sides.

$$z^{2}-9-16=0$$

Subtract 16 from -9 to get -25.

$$z^{2}-25=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -25 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$z=\frac{0±\sqrt{0^{2}-4\left(-25\right)}}{2}$$

Square 0.

$$z=\frac{0±\sqrt{-4\left(-25\right)}}{2}$$

Multiply -4 times -25.

$$z=\frac{0±\sqrt{100}}{2}$$

Take the square root of 100.

$$z=\frac{0±10}{2}$$

Now solve the equation z=\frac{0±10}{2} when ± is plus. Divide 10 by 2.

$$z=5$$

Now solve the equation z=\frac{0±10}{2} when ± is minus. Divide -10 by 2.

$$z=-5$$

The equation is now solved.

$$z=5 z=-5$$