Solve 18a^2=8

$$18 a ^ { 2 } = 8$$

Solve for a

$$a=\frac{2}{3}\approx 0.666666667$$

$$a=-\frac{2}{3}\approx -0.666666667$$

Steps Using Difference of Squares

Divide both sides by 18.

$$a^{2}=\frac{8}{18}$$

Reduce the fraction \frac{8}{18} to lowest terms by extracting and canceling out 2.

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

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

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

Multiply both sides by 9.

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

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

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

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

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

Steps by Finding Square Root

Divide both sides by 18.

$$a^{2}=\frac{8}{18}$$

Reduce the fraction \frac{8}{18} to lowest terms by extracting and canceling out 2.

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

Take the square root of both sides of the equation.

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

Steps Using the Quadratic Formula

Divide both sides by 18.

$$a^{2}=\frac{8}{18}$$

Reduce the fraction \frac{8}{18} to lowest terms by extracting and canceling out 2.

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

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

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

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

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

Square 0.

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

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

$$a=\frac{0±\sqrt{\frac{16}{9}}}{2}$$

Take the square root of \frac{16}{9}.

$$a=\frac{0±\frac{4}{3}}{2}$$

Now solve the equation a=\frac{0±\frac{4}{3}}{2} when ± is plus.

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

Now solve the equation a=\frac{0±\frac{4}{3}}{2} when ± is minus.

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

The equation is now solved.

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