Solve 0=20-p^2

$$0 = 20 - p ^ { 2 }$$

Solve for p

$$p=2\sqrt{5}\approx 4.472135955$$

$$p=-2\sqrt{5}\approx -4.472135955$$

Steps by Finding Square Root

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

$$20-p^{2}=0$$

Subtract 20 from both sides. Anything subtracted from zero gives its negation.

$$-p^{2}=-20$$

Divide both sides by -1.

$$p^{2}=\frac{-20}{-1}$$

Fraction \frac{-20}{-1} can be simplified to 20 by removing the negative sign from both the numerator and the denominator.

$$p^{2}=20$$

Take the square root of both sides of the equation.

$$p=2\sqrt{5} p=-2\sqrt{5}$$

Steps Using the Quadratic Formula

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

$$20-p^{2}=0$$

Quadratic equations like this one, with an x^{2} term but no x term, can still be solved using the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}, once they are put in standard form: ax^{2}+bx+c=0.

$$-p^{2}+20=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -1 for a, 0 for b, and 20 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$p=\frac{0±\sqrt{0^{2}-4\left(-1\right)\times 20}}{2\left(-1\right)}$$

Square 0.

$$p=\frac{0±\sqrt{-4\left(-1\right)\times 20}}{2\left(-1\right)}$$

Multiply -4 times -1.

$$p=\frac{0±\sqrt{4\times 20}}{2\left(-1\right)}$$

Multiply 4 times 20.

$$p=\frac{0±\sqrt{80}}{2\left(-1\right)}$$

Take the square root of 80.

$$p=\frac{0±4\sqrt{5}}{2\left(-1\right)}$$

Multiply 2 times -1.

$$p=\frac{0±4\sqrt{5}}{-2}$$

Now solve the equation p=\frac{0±4\sqrt{5}}{-2} when ± is plus.

$$p=-2\sqrt{5}$$

Now solve the equation p=\frac{0±4\sqrt{5}}{-2} when ± is minus.

$$p=2\sqrt{5}$$

The equation is now solved.

$$p=-2\sqrt{5} p=2\sqrt{5}$$