Solve 72=32q^2

$$72 = 32 q ^ { 2 }$$

Solve for q

$$q = \frac{3}{2} = 1\frac{1}{2} = 1.5$$

$$q = -\frac{3}{2} = -1\frac{1}{2} = -1.5$$

Steps Using Difference of Squares

Divide both sides by 32.

$$\frac{72}{32}=q^{2}$$

Reduce the fraction \frac{72}{32} to lowest terms by extracting and canceling out 8.

$$\frac{9}{4}=q^{2}$$

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

$$q^{2}=\frac{9}{4}$$

Subtract \frac{9}{4} from both sides.

$$q^{2}-\frac{9}{4}=0$$

Multiply both sides by 4.

$$4q^{2}-9=0$$

Consider 4q^{2}-9. Rewrite 4q^{2}-9 as \left(2q\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).

$$\left(2q-3\right)\left(2q+3\right)=0$$

To find equation solutions, solve 2q-3=0 and 2q+3=0.

$$q=\frac{3}{2} q=-\frac{3}{2}$$

Steps by Finding Square Root

Divide both sides by 32.

$$\frac{72}{32}=q^{2}$$

Reduce the fraction \frac{72}{32} to lowest terms by extracting and canceling out 8.

$$\frac{9}{4}=q^{2}$$

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

$$q^{2}=\frac{9}{4}$$

Take the square root of both sides of the equation.

$$q=\frac{3}{2} q=-\frac{3}{2}$$

Steps Using the Quadratic Formula

Divide both sides by 32.

$$\frac{72}{32}=q^{2}$$

Reduce the fraction \frac{72}{32} to lowest terms by extracting and canceling out 8.

$$\frac{9}{4}=q^{2}$$

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

$$q^{2}=\frac{9}{4}$$

Subtract \frac{9}{4} from both sides.

$$q^{2}-\frac{9}{4}=0$$

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

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

Square 0.

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

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

$$q=\frac{0±\sqrt{9}}{2}$$

Take the square root of 9.

$$q=\frac{0±3}{2}$$

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

$$q=\frac{3}{2}$$

Now solve the equation q=\frac{0±3}{2} when ± is minus. Divide -3 by 2.

$$q=-\frac{3}{2}$$

The equation is now solved.

$$q=\frac{3}{2} q=-\frac{3}{2}$$