Solve 120=4p^2+400

$$120 = 4 p ^ { 2 } + 400$$

Solve for p

$$p=-\sqrt{70}i\approx -0-8.366600265i$$

$$p=\sqrt{70}i\approx 8.366600265i$$

Steps by Finding Square Root

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

$$4p^{2}+400=120$$

Subtract 400 from both sides.

$$4p^{2}=120-400$$

Subtract 400 from 120 to get -280.

$$4p^{2}=-280$$

Divide both sides by 4.

$$p^{2}=\frac{-280}{4}$$

Divide -280 by 4 to get -70.

$$p^{2}=-70$$

The equation is now solved.

$$p=\sqrt{70}i p=-\sqrt{70}i$$

Steps Using the Quadratic Formula

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

$$4p^{2}+400=120$$

Subtract 120 from both sides.

$$4p^{2}+400-120=0$$

Subtract 120 from 400 to get 280.

$$4p^{2}+280=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 4 for a, 0 for b, and 280 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$p=\frac{0±\sqrt{0^{2}-4\times 4\times 280}}{2\times 4}$$

Square 0.

$$p=\frac{0±\sqrt{-4\times 4\times 280}}{2\times 4}$$

Multiply -4 times 4.

$$p=\frac{0±\sqrt{-16\times 280}}{2\times 4}$$

Multiply -16 times 280.

$$p=\frac{0±\sqrt{-4480}}{2\times 4}$$

Take the square root of -4480.

$$p=\frac{0±8\sqrt{70}i}{2\times 4}$$

Multiply 2 times 4.

$$p=\frac{0±8\sqrt{70}i}{8}$$

Now solve the equation p=\frac{0±8\sqrt{70}i}{8} when ± is plus.

$$p=\sqrt{70}i$$

Now solve the equation p=\frac{0±8\sqrt{70}i}{8} when ± is minus.

$$p=-\sqrt{70}i$$

The equation is now solved.

$$p=\sqrt{70}i p=-\sqrt{70}i$$