Solve 3u^2=1/3

$$3 u ^ { 2 } = \frac { 1 } { 3 }$$

Solve for u

$$u=\frac{1}{3}\approx 0.333333333$$

$$u=-\frac{1}{3}\approx -0.333333333$$

Steps Using Difference of Squares

Divide both sides by 3.

$$u^{2}=\frac{\frac{1}{3}}{3}$$

Express \frac{\frac{1}{3}}{3} as a single fraction.

$$u^{2}=\frac{1}{3\times 3}$$

Multiply 3 and 3 to get 9.

$$u^{2}=\frac{1}{9}$$

Subtract \frac{1}{9} from both sides.

$$u^{2}-\frac{1}{9}=0$$

Multiply both sides by 9.

$$9u^{2}-1=0$$

Consider 9u^{2}-1. Rewrite 9u^{2}-1 as \left(3u\right)^{2}-1^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(3u-1\right)\left(3u+1\right)=0$$

To find equation solutions, solve 3u-1=0 and 3u+1=0.

$$u=\frac{1}{3} u=-\frac{1}{3}$$

Steps by Finding Square Root

Divide both sides by 3.

$$u^{2}=\frac{\frac{1}{3}}{3}$$

Express \frac{\frac{1}{3}}{3} as a single fraction.

$$u^{2}=\frac{1}{3\times 3}$$

Multiply 3 and 3 to get 9.

$$u^{2}=\frac{1}{9}$$

Take the square root of both sides of the equation.

$$u=\frac{1}{3} u=-\frac{1}{3}$$

Steps Using the Quadratic Formula

Divide both sides by 3.

$$u^{2}=\frac{\frac{1}{3}}{3}$$

Express \frac{\frac{1}{3}}{3} as a single fraction.

$$u^{2}=\frac{1}{3\times 3}$$

Multiply 3 and 3 to get 9.

$$u^{2}=\frac{1}{9}$$

Subtract \frac{1}{9} from both sides.

$$u^{2}-\frac{1}{9}=0$$

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

$$u=\frac{0±\sqrt{0^{2}-4\left(-\frac{1}{9}\right)}}{2}$$

Square 0.

$$u=\frac{0±\sqrt{-4\left(-\frac{1}{9}\right)}}{2}$$

Multiply -4 times -\frac{1}{9}.

$$u=\frac{0±\sqrt{\frac{4}{9}}}{2}$$

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

$$u=\frac{0±\frac{2}{3}}{2}$$

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

$$u=\frac{1}{3}$$

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

$$u=-\frac{1}{3}$$

The equation is now solved.

$$u=\frac{1}{3} u=-\frac{1}{3}$$