Solve 5p^2=7p^2-18

$$5 p ^ { 2 } = 7 p ^ { 2 } - 18$$

Solve for p

$$p=3$$

$$p=-3$$

Steps by Finding Square Root

Subtract 7p^{2} from both sides.

$$5p^{2}-7p^{2}=-18$$

Combine 5p^{2} and -7p^{2} to get -2p^{2}.

$$-2p^{2}=-18$$

Divide both sides by -2.

$$p^{2}=\frac{-18}{-2}$$

Divide -18 by -2 to get 9.

$$p^{2}=9$$

Take the square root of both sides of the equation.

$$p=3 p=-3$$

Steps Using the Quadratic Formula

Subtract 7p^{2} from both sides.

$$5p^{2}-7p^{2}=-18$$

Combine 5p^{2} and -7p^{2} to get -2p^{2}.

$$-2p^{2}=-18$$

Add 18 to both sides.

$$-2p^{2}+18=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -2 for a, 0 for b, and 18 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$p=\frac{0±\sqrt{0^{2}-4\left(-2\right)\times 18}}{2\left(-2\right)}$$

Square 0.

$$p=\frac{0±\sqrt{-4\left(-2\right)\times 18}}{2\left(-2\right)}$$

Multiply -4 times -2.

$$p=\frac{0±\sqrt{8\times 18}}{2\left(-2\right)}$$

Multiply 8 times 18.

$$p=\frac{0±\sqrt{144}}{2\left(-2\right)}$$

Take the square root of 144.

$$p=\frac{0±12}{2\left(-2\right)}$$

Multiply 2 times -2.

$$p=\frac{0±12}{-4}$$

Now solve the equation p=\frac{0±12}{-4} when ± is plus. Divide 12 by -4.

$$p=-3$$

Now solve the equation p=\frac{0±12}{-4} when ± is minus. Divide -12 by -4.

$$p=3$$

The equation is now solved.

$$p=-3 p=3$$