Solve 18y^2=32

$$18 y ^ { 2 } = 32$$

Solve for y

$$y = \frac{4}{3} = 1\frac{1}{3} \approx 1.333333333$$

$$y = -\frac{4}{3} = -1\frac{1}{3} \approx -1.333333333$$

Steps Using Difference of Squares

Divide both sides by 18.

$$y^{2}=\frac{32}{18}$$

Reduce the fraction \frac{32}{18} to lowest terms by extracting and canceling out 2.

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

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

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

Multiply both sides by 9.

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

Consider 9y^{2}-16. Rewrite 9y^{2}-16 as \left(3y\right)^{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).

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

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

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

Steps by Finding Square Root

Divide both sides by 18.

$$y^{2}=\frac{32}{18}$$

Reduce the fraction \frac{32}{18} to lowest terms by extracting and canceling out 2.

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

Take the square root of both sides of the equation.

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

Steps Using the Quadratic Formula

Divide both sides by 18.

$$y^{2}=\frac{32}{18}$$

Reduce the fraction \frac{32}{18} to lowest terms by extracting and canceling out 2.

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

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

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

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

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

Square 0.

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

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

$$y=\frac{0±\sqrt{\frac{64}{9}}}{2}$$

Take the square root of \frac{64}{9}.

$$y=\frac{0±\frac{8}{3}}{2}$$

Now solve the equation y=\frac{0±\frac{8}{3}}{2} when ± is plus.

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

Now solve the equation y=\frac{0±\frac{8}{3}}{2} when ± is minus.

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

The equation is now solved.

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