Solve 4P^2=1/4+1/12

$$4 P ^ { 2 } = 1 / 4 + 1 / 12$$

Solve for P

$$P=\frac{\sqrt{3}}{6}\approx 0.288675135$$

$$P=-\frac{\sqrt{3}}{6}\approx -0.288675135$$

Steps by Finding Square Root

Add \frac{1}{4} and \frac{1}{12} to get \frac{1}{3}.

$$4P^{2}=\frac{1}{3}$$

Divide both sides by 4.

$$P^{2}=\frac{\frac{1}{3}}{4}$$

Express \frac{\frac{1}{3}}{4} as a single fraction.

$$P^{2}=\frac{1}{3\times 4}$$

Multiply 3 and 4 to get 12.

$$P^{2}=\frac{1}{12}$$

Take the square root of both sides of the equation.

$$P=\frac{\sqrt{3}}{6} P=-\frac{\sqrt{3}}{6}$$

Steps Using the Quadratic Formula

Add \frac{1}{4} and \frac{1}{12} to get \frac{1}{3}.

$$4P^{2}=\frac{1}{3}$$

Subtract \frac{1}{3} from both sides.

$$4P^{2}-\frac{1}{3}=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 4 for a, 0 for b, and -\frac{1}{3} for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$P=\frac{0±\sqrt{0^{2}-4\times 4\left(-\frac{1}{3}\right)}}{2\times 4}$$

Square 0.

$$P=\frac{0±\sqrt{-4\times 4\left(-\frac{1}{3}\right)}}{2\times 4}$$

Multiply -4 times 4.

$$P=\frac{0±\sqrt{-16\left(-\frac{1}{3}\right)}}{2\times 4}$$

Multiply -16 times -\frac{1}{3}.

$$P=\frac{0±\sqrt{\frac{16}{3}}}{2\times 4}$$

Take the square root of \frac{16}{3}.

$$P=\frac{0±\frac{4\sqrt{3}}{3}}{2\times 4}$$

Multiply 2 times 4.

$$P=\frac{0±\frac{4\sqrt{3}}{3}}{8}$$

Now solve the equation P=\frac{0±\frac{4\sqrt{3}}{3}}{8} when ± is plus.

$$P=\frac{\sqrt{3}}{6}$$

Now solve the equation P=\frac{0±\frac{4\sqrt{3}}{3}}{8} when ± is minus.

$$P=-\frac{\sqrt{3}}{6}$$

The equation is now solved.

$$P=\frac{\sqrt{3}}{6} P=-\frac{\sqrt{3}}{6}$$