Solve p^2/2-4p^2=-14

$$\frac { p ^ { 2 } } { 2 } - 4 p ^ { 2 } = - 14$$

Solve for p

$$p=2$$

$$p=-2$$

Steps by Finding Square Root

Multiply both sides of the equation by 2.

$$p^{2}-8p^{2}=-28$$

Combine p^{2} and -8p^{2} to get -7p^{2}.

$$-7p^{2}=-28$$

Divide both sides by -7.

$$p^{2}=\frac{-28}{-7}$$

Divide -28 by -7 to get 4.

$$p^{2}=4$$

Take the square root of both sides of the equation.

$$p=2 p=-2$$

Steps Using the Quadratic Formula

Multiply both sides of the equation by 2.

$$p^{2}-8p^{2}=-28$$

Combine p^{2} and -8p^{2} to get -7p^{2}.

$$-7p^{2}=-28$$

Add 28 to both sides.

$$-7p^{2}+28=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -7 for a, 0 for b, and 28 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$p=\frac{0±\sqrt{0^{2}-4\left(-7\right)\times 28}}{2\left(-7\right)}$$

Square 0.

$$p=\frac{0±\sqrt{-4\left(-7\right)\times 28}}{2\left(-7\right)}$$

Multiply -4 times -7.

$$p=\frac{0±\sqrt{28\times 28}}{2\left(-7\right)}$$

Multiply 28 times 28.

$$p=\frac{0±\sqrt{784}}{2\left(-7\right)}$$

Take the square root of 784.

$$p=\frac{0±28}{2\left(-7\right)}$$

Multiply 2 times -7.

$$p=\frac{0±28}{-14}$$

Now solve the equation p=\frac{0±28}{-14} when ± is plus. Divide 28 by -14.

$$p=-2$$

Now solve the equation p=\frac{0±28}{-14} when ± is minus. Divide -28 by -14.

$$p=2$$

The equation is now solved.

$$p=-2 p=2$$