p^2+16p=-22

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Solution for p^2+16p=-22 equation:


Simplifying
p2 + 16p = -22

Reorder the terms:
16p + p2 = -22

Solving
16p + p2 = -22

Solving for variable 'p'.

Reorder the terms:
22 + 16p + p2 = -22 + 22

Combine like terms: -22 + 22 = 0
22 + 16p + p2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-22' to each side of the equation.
22 + 16p + -22 + p2 = 0 + -22

Reorder the terms:
22 + -22 + 16p + p2 = 0 + -22

Combine like terms: 22 + -22 = 0
0 + 16p + p2 = 0 + -22
16p + p2 = 0 + -22

Combine like terms: 0 + -22 = -22
16p + p2 = -22

The p term is 16p.  Take half its coefficient (8).
Square it (64) and add it to both sides.

Add '64' to each side of the equation.
16p + 64 + p2 = -22 + 64

Reorder the terms:
64 + 16p + p2 = -22 + 64

Combine like terms: -22 + 64 = 42
64 + 16p + p2 = 42

Factor a perfect square on the left side:
(p + 8)(p + 8) = 42

Calculate the square root of the right side: 6.480740698

Break this problem into two subproblems by setting 
(p + 8) equal to 6.480740698 and -6.480740698.

Subproblem 1

p + 8 = 6.480740698 Simplifying p + 8 = 6.480740698 Reorder the terms: 8 + p = 6.480740698 Solving 8 + p = 6.480740698 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + p = 6.480740698 + -8 Combine like terms: 8 + -8 = 0 0 + p = 6.480740698 + -8 p = 6.480740698 + -8 Combine like terms: 6.480740698 + -8 = -1.519259302 p = -1.519259302 Simplifying p = -1.519259302

Subproblem 2

p + 8 = -6.480740698 Simplifying p + 8 = -6.480740698 Reorder the terms: 8 + p = -6.480740698 Solving 8 + p = -6.480740698 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + p = -6.480740698 + -8 Combine like terms: 8 + -8 = 0 0 + p = -6.480740698 + -8 p = -6.480740698 + -8 Combine like terms: -6.480740698 + -8 = -14.480740698 p = -14.480740698 Simplifying p = -14.480740698

Solution

The solution to the problem is based on the solutions from the subproblems. p = {-1.519259302, -14.480740698}

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