Solve 100/3-25=p^2

$$\frac { 100 } { 3 } - 25 = p ^ { 2 }$$

Solve for p

$$p = \frac{5 \sqrt{3}}{3} \approx 2.886751346$$

$$p = -\frac{5 \sqrt{3}}{3} \approx -2.886751346$$

Steps by Finding Square Root

Subtract 25 from \frac{100}{3} to get \frac{25}{3}.

$$\frac{25}{3}=p^{2}$$

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

$$p^{2}=\frac{25}{3}$$

Take the square root of both sides of the equation.

$$p=\frac{5\sqrt{3}}{3} p=-\frac{5\sqrt{3}}{3}$$

Steps Using the Quadratic Formula

Subtract 25 from \frac{100}{3} to get \frac{25}{3}.

$$\frac{25}{3}=p^{2}$$

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

$$p^{2}=\frac{25}{3}$$

Subtract \frac{25}{3} from both sides.

$$p^{2}-\frac{25}{3}=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -\frac{25}{3} for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$p=\frac{0±\sqrt{0^{2}-4\left(-\frac{25}{3}\right)}}{2}$$

Square 0.

$$p=\frac{0±\sqrt{-4\left(-\frac{25}{3}\right)}}{2}$$

Multiply -4 times -\frac{25}{3}.

$$p=\frac{0±\sqrt{\frac{100}{3}}}{2}$$

Take the square root of \frac{100}{3}.

$$p=\frac{0±\frac{10\sqrt{3}}{3}}{2}$$

Now solve the equation p=\frac{0±\frac{10\sqrt{3}}{3}}{2} when ± is plus.

$$p=\frac{5\sqrt{3}}{3}$$

Now solve the equation p=\frac{0±\frac{10\sqrt{3}}{3}}{2} when ± is minus.

$$p=-\frac{5\sqrt{3}}{3}$$

The equation is now solved.

$$p=\frac{5\sqrt{3}}{3} p=-\frac{5\sqrt{3}}{3}$$