p^2+5p-85=0

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Solution for p^2+5p-85=0 equation: 


Simplifying
p2 + 5p + -85 = 0

Reorder the terms:
-85 + 5p + p2 = 0

Solving
-85 + 5p + p2 = 0

Solving for variable 'p'.

Begin completing the square.

Move the constant term to the right:

Add '85' to each side of the equation.
-85 + 5p + 85 + p2 = 0 + 85

Reorder the terms:
-85 + 85 + 5p + p2 = 0 + 85

Combine like terms: -85 + 85 = 0
0 + 5p + p2 = 0 + 85
5p + p2 = 0 + 85

Combine like terms: 0 + 85 = 85
5p + p2 = 85

The p term is 5p.  Take half its coefficient (2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
5p + 6.25 + p2 = 85 + 6.25

Reorder the terms:
6.25 + 5p + p2 = 85 + 6.25

Combine like terms: 85 + 6.25 = 91.25
6.25 + 5p + p2 = 91.25

Factor a perfect square on the left side:
(p + 2.5)(p + 2.5) = 91.25

Calculate the square root of the right side: 9.552486587

Break this problem into two subproblems by setting 
(p + 2.5) equal to 9.552486587 and -9.552486587.


Subproblem 1
p + 2.5 = 9.552486587

Simplifying
p + 2.5 = 9.552486587

Reorder the terms:
2.5 + p = 9.552486587

Solving
2.5 + p = 9.552486587

Solving for variable 'p'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + p = 9.552486587 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + p = 9.552486587 + -2.5
p = 9.552486587 + -2.5

Combine like terms: 9.552486587 + -2.5 = 7.052486587
p = 7.052486587

Simplifying
p = 7.052486587


Subproblem 2
p + 2.5 = -9.552486587

Simplifying
p + 2.5 = -9.552486587

Reorder the terms:
2.5 + p = -9.552486587

Solving
2.5 + p = -9.552486587

Solving for variable 'p'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + p = -9.552486587 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + p = -9.552486587 + -2.5
p = -9.552486587 + -2.5

Combine like terms: -9.552486587 + -2.5 = -12.052486587
p = -12.052486587

Simplifying
p = -12.052486587


Solution
The solution to the problem is based on the solutions
from the subproblems.
p = {7.052486587, -12.052486587}

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