p^2+5p-120=0

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Solution for p^2+5p-120=0 equation: 


Simplifying
p2 + 5p + -120 = 0

Reorder the terms:
-120 + 5p + p2 = 0

Solving
-120 + 5p + p2 = 0

Solving for variable 'p'.

Begin completing the square.

Move the constant term to the right:

Add '120' to each side of the equation.
-120 + 5p + 120 + p2 = 0 + 120

Reorder the terms:
-120 + 120 + 5p + p2 = 0 + 120

Combine like terms: -120 + 120 = 0
0 + 5p + p2 = 0 + 120
5p + p2 = 0 + 120

Combine like terms: 0 + 120 = 120
5p + p2 = 120

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 = 120 + 6.25

Reorder the terms:
6.25 + 5p + p2 = 120 + 6.25

Combine like terms: 120 + 6.25 = 126.25
6.25 + 5p + p2 = 126.25

Factor a perfect square on the left side:
(p + 2.5)(p + 2.5) = 126.25

Calculate the square root of the right side: 11.236102527

Break this problem into two subproblems by setting 
(p + 2.5) equal to 11.236102527 and -11.236102527.


Subproblem 1
p + 2.5 = 11.236102527

Simplifying
p + 2.5 = 11.236102527

Reorder the terms:
2.5 + p = 11.236102527

Solving
2.5 + p = 11.236102527

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 = 11.236102527 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + p = 11.236102527 + -2.5
p = 11.236102527 + -2.5

Combine like terms: 11.236102527 + -2.5 = 8.736102527
p = 8.736102527

Simplifying
p = 8.736102527


Subproblem 2
p + 2.5 = -11.236102527

Simplifying
p + 2.5 = -11.236102527

Reorder the terms:
2.5 + p = -11.236102527

Solving
2.5 + p = -11.236102527

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 = -11.236102527 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + p = -11.236102527 + -2.5
p = -11.236102527 + -2.5

Combine like terms: -11.236102527 + -2.5 = -13.736102527
p = -13.736102527

Simplifying
p = -13.736102527


Solution
The solution to the problem is based on the solutions
from the subproblems.
p = {8.736102527, -13.736102527}

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