Solve 4p^2-44=-8

$$4 p ^ { 2 } - 44 = - 8$$

Solve for p

$$p=3$$

$$p=-3$$

Steps Using Difference of Squares

Add 8 to both sides.

$$4p^{2}-44+8=0$$

Add -44 and 8 to get -36.

$$4p^{2}-36=0$$

Divide both sides by 4.

$$p^{2}-9=0$$

Consider p^{2}-9. Rewrite p^{2}-9 as p^{2}-3^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(p-3\right)\left(p+3\right)=0$$

To find equation solutions, solve p-3=0 and p+3=0.

$$p=3 p=-3$$

Steps by Finding Square Root

Add 44 to both sides.

$$4p^{2}=-8+44$$

Add -8 and 44 to get 36.

$$4p^{2}=36$$

Divide both sides by 4.

$$p^{2}=\frac{36}{4}$$

Divide 36 by 4 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

Add 8 to both sides.

$$4p^{2}-44+8=0$$

Add -44 and 8 to get -36.

$$4p^{2}-36=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 4 for a, 0 for b, and -36 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$p=\frac{0±\sqrt{0^{2}-4\times 4\left(-36\right)}}{2\times 4}$$

Square 0.

$$p=\frac{0±\sqrt{-4\times 4\left(-36\right)}}{2\times 4}$$

Multiply -4 times 4.

$$p=\frac{0±\sqrt{-16\left(-36\right)}}{2\times 4}$$

Multiply -16 times -36.

$$p=\frac{0±\sqrt{576}}{2\times 4}$$

Take the square root of 576.

$$p=\frac{0±24}{2\times 4}$$

Multiply 2 times 4.

$$p=\frac{0±24}{8}$$

Now solve the equation p=\frac{0±24}{8} when ± is plus. Divide 24 by 8.

$$p=3$$

Now solve the equation p=\frac{0±24}{8} when ± is minus. Divide -24 by 8.

$$p=-3$$

The equation is now solved.

$$p=3 p=-3$$