p^2-15p-144=0

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Solution for p^2-15p-144=0 equation: 


Simplifying
p2 + -15p + -144 = 0

Reorder the terms:
-144 + -15p + p2 = 0

Solving
-144 + -15p + p2 = 0

Solving for variable 'p'.

Begin completing the square.

Move the constant term to the right:

Add '144' to each side of the equation.
-144 + -15p + 144 + p2 = 0 + 144

Reorder the terms:
-144 + 144 + -15p + p2 = 0 + 144

Combine like terms: -144 + 144 = 0
0 + -15p + p2 = 0 + 144
-15p + p2 = 0 + 144

Combine like terms: 0 + 144 = 144
-15p + p2 = 144

The p term is -15p.  Take half its coefficient (-7.5).
Square it (56.25) and add it to both sides.

Add '56.25' to each side of the equation.
-15p + 56.25 + p2 = 144 + 56.25

Reorder the terms:
56.25 + -15p + p2 = 144 + 56.25

Combine like terms: 144 + 56.25 = 200.25
56.25 + -15p + p2 = 200.25

Factor a perfect square on the left side:
(p + -7.5)(p + -7.5) = 200.25

Calculate the square root of the right side: 14.150971698

Break this problem into two subproblems by setting 
(p + -7.5) equal to 14.150971698 and -14.150971698.


Subproblem 1
p + -7.5 = 14.150971698

Simplifying
p + -7.5 = 14.150971698

Reorder the terms:
-7.5 + p = 14.150971698

Solving
-7.5 + p = 14.150971698

Solving for variable 'p'.

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

Add '7.5' to each side of the equation.
-7.5 + 7.5 + p = 14.150971698 + 7.5

Combine like terms: -7.5 + 7.5 = 0.0
0.0 + p = 14.150971698 + 7.5
p = 14.150971698 + 7.5

Combine like terms: 14.150971698 + 7.5 = 21.650971698
p = 21.650971698

Simplifying
p = 21.650971698


Subproblem 2
p + -7.5 = -14.150971698

Simplifying
p + -7.5 = -14.150971698

Reorder the terms:
-7.5 + p = -14.150971698

Solving
-7.5 + p = -14.150971698

Solving for variable 'p'.

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

Add '7.5' to each side of the equation.
-7.5 + 7.5 + p = -14.150971698 + 7.5

Combine like terms: -7.5 + 7.5 = 0.0
0.0 + p = -14.150971698 + 7.5
p = -14.150971698 + 7.5

Combine like terms: -14.150971698 + 7.5 = -6.650971698
p = -6.650971698

Simplifying
p = -6.650971698


Solution
The solution to the problem is based on the solutions
from the subproblems.
p = {21.650971698, -6.650971698}

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