Solve p^2+8p+6=6

$$p ^ { 2 } + 8 p + 6 = 6$$

Solve for p

$$p=-8$$

$$p=0$$

Steps Using Factoring

Subtract 6 from both sides.

$$p^{2}+8p+6-6=0$$

Subtract 6 from 6 to get 0.

$$p^{2}+8p=0$$

Factor out p.

$$p\left(p+8\right)=0$$

To find equation solutions, solve p=0 and p+8=0.

$$p=0 p=-8$$

Steps Using the Quadratic Formula

All equations of the form ax^{2}+bx+c=0 can be solved using the quadratic formula: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. The quadratic formula gives two solutions, one when ± is addition and one when it is subtraction.

$$p^{2}+8p+6=6$$

Subtract 6 from both sides of the equation.

$$p^{2}+8p+6-6=6-6$$

Subtracting 6 from itself leaves 0.

$$p^{2}+8p+6-6=0$$

Subtract 6 from 6.

$$p^{2}+8p=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 8 for b, and 0 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$p=\frac{-8±\sqrt{8^{2}}}{2}$$

Take the square root of 8^{2}.

$$p=\frac{-8±8}{2}$$

Now solve the equation p=\frac{-8±8}{2} when ± is plus. Add -8 to 8.

$$p=\frac{0}{2}$$

Divide 0 by 2.

$$p=0$$

Now solve the equation p=\frac{-8±8}{2} when ± is minus. Subtract 8 from -8.

$$p=-\frac{16}{2}$$

Divide -16 by 2.

$$p=-8$$

The equation is now solved.

$$p=0 p=-8$$

Steps for Completing the Square

Subtract 6 from both sides.

$$p^{2}+8p+6-6=0$$

Subtract 6 from 6 to get 0.

$$p^{2}+8p=0$$

Divide 8, the coefficient of the x term, by 2 to get 4. Then add the square of 4 to both sides of the equation. This step makes the left hand side of the equation a perfect square.

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

Square 4.

$$p^{2}+8p+16=16$$

Factor p^{2}+8p+16. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(p+4\right)^{2}=16$$

Take the square root of both sides of the equation.

$$\sqrt{\left(p+4\right)^{2}}=\sqrt{16}$$

Simplify.

$$p+4=4 p+4=-4$$

Subtract 4 from both sides of the equation.

$$p=0 p=-8$$