Solve 4p^2-7=13

$$4 p ^ { 2 } - 7 = 13$$

Solve for p

$$p=\sqrt{5}\approx 2.236067977$$

$$p=-\sqrt{5}\approx -2.236067977$$

Steps by Finding Square Root

Add 7 to both sides.

$$4p^{2}=13+7$$

Add 13 and 7 to get 20.

$$4p^{2}=20$$

Divide both sides by 4.

$$p^{2}=\frac{20}{4}$$

Divide 20 by 4 to get 5.

$$p^{2}=5$$

Take the square root of both sides of the equation.

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

Steps Using the Quadratic Formula

Subtract 13 from both sides.

$$4p^{2}-7-13=0$$

Subtract 13 from -7 to get -20.

$$4p^{2}-20=0$$

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

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

Square 0.

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

Multiply -4 times 4.

$$p=\frac{0±\sqrt{-16\left(-20\right)}}{2\times 4}$$

Multiply -16 times -20.

$$p=\frac{0±\sqrt{320}}{2\times 4}$$

Take the square root of 320.

$$p=\frac{0±8\sqrt{5}}{2\times 4}$$

Multiply 2 times 4.

$$p=\frac{0±8\sqrt{5}}{8}$$

Now solve the equation p=\frac{0±8\sqrt{5}}{8} when ± is plus.

$$p=\sqrt{5}$$

Now solve the equation p=\frac{0±8\sqrt{5}}{8} when ± is minus.

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

The equation is now solved.

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