Solve 16r^2=9

$$16 r ^ { 2 } = 9$$

Solve for r

$$r=\frac{3}{4}=0.75$$

$$r=-\frac{3}{4}=-0.75$$

Steps Using Difference of Squares

Divide both sides by 16.

$$r^{2}=\frac{9}{16}$$

Subtract \frac{9}{16} from both sides.

$$r^{2}-\frac{9}{16}=0$$

Multiply both sides by 16.

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

Consider 16r^{2}-9. Rewrite 16r^{2}-9 as \left(4r\right)^{2}-3^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(4r-3\right)\left(4r+3\right)=0$$

To find equation solutions, solve 4r-3=0 and 4r+3=0.

$$r=\frac{3}{4} r=-\frac{3}{4}$$

Steps by Finding Square Root

Divide both sides by 16.

$$r^{2}=\frac{9}{16}$$

Take the square root of both sides of the equation.

$$r=\frac{3}{4} r=-\frac{3}{4}$$

Steps Using the Quadratic Formula

Divide both sides by 16.

$$r^{2}=\frac{9}{16}$$

Subtract \frac{9}{16} from both sides.

$$r^{2}-\frac{9}{16}=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -\frac{9}{16} for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$r=\frac{0±\sqrt{0^{2}-4\left(-\frac{9}{16}\right)}}{2}$$

Square 0.

$$r=\frac{0±\sqrt{-4\left(-\frac{9}{16}\right)}}{2}$$

Multiply -4 times -\frac{9}{16}.

$$r=\frac{0±\sqrt{\frac{9}{4}}}{2}$$

Take the square root of \frac{9}{4}.

$$r=\frac{0±\frac{3}{2}}{2}$$

Now solve the equation r=\frac{0±\frac{3}{2}}{2} when ± is plus.

$$r=\frac{3}{4}$$

Now solve the equation r=\frac{0±\frac{3}{2}}{2} when ± is minus.

$$r=-\frac{3}{4}$$

The equation is now solved.

$$r=\frac{3}{4} r=-\frac{3}{4}$$