p^2+22p-5=0

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Solution for p^2+22p-5=0 equation: 


Simplifying
p2 + 22p + -5 = 0

Reorder the terms:
-5 + 22p + p2 = 0

Solving
-5 + 22p + p2 = 0

Solving for variable 'p'.

Begin completing the square.

Move the constant term to the right:

Add '5' to each side of the equation.
-5 + 22p + 5 + p2 = 0 + 5

Reorder the terms:
-5 + 5 + 22p + p2 = 0 + 5

Combine like terms: -5 + 5 = 0
0 + 22p + p2 = 0 + 5
22p + p2 = 0 + 5

Combine like terms: 0 + 5 = 5
22p + p2 = 5

The p term is 22p.  Take half its coefficient (11).
Square it (121) and add it to both sides.

Add '121' to each side of the equation.
22p + 121 + p2 = 5 + 121

Reorder the terms:
121 + 22p + p2 = 5 + 121

Combine like terms: 5 + 121 = 126
121 + 22p + p2 = 126

Factor a perfect square on the left side:
(p + 11)(p + 11) = 126

Calculate the square root of the right side: 11.22497216

Break this problem into two subproblems by setting 
(p + 11) equal to 11.22497216 and -11.22497216.


Subproblem 1
p + 11 = 11.22497216

Simplifying
p + 11 = 11.22497216

Reorder the terms:
11 + p = 11.22497216

Solving
11 + p = 11.22497216

Solving for variable 'p'.

Move all terms containing p to the left, all other terms to the right.

Add '-11' to each side of the equation.
11 + -11 + p = 11.22497216 + -11

Combine like terms: 11 + -11 = 0
0 + p = 11.22497216 + -11
p = 11.22497216 + -11

Combine like terms: 11.22497216 + -11 = 0.22497216
p = 0.22497216

Simplifying
p = 0.22497216


Subproblem 2
p + 11 = -11.22497216

Simplifying
p + 11 = -11.22497216

Reorder the terms:
11 + p = -11.22497216

Solving
11 + p = -11.22497216

Solving for variable 'p'.

Move all terms containing p to the left, all other terms to the right.

Add '-11' to each side of the equation.
11 + -11 + p = -11.22497216 + -11

Combine like terms: 11 + -11 = 0
0 + p = -11.22497216 + -11
p = -11.22497216 + -11

Combine like terms: -11.22497216 + -11 = -22.22497216
p = -22.22497216

Simplifying
p = -22.22497216


Solution
The solution to the problem is based on the solutions
from the subproblems.
p = {0.22497216, -22.22497216}

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