p^2+260p-500=0

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Solution for p^2+260p-500=0 equation: 


Simplifying
p2 + 260p + -500 = 0

Reorder the terms:
-500 + 260p + p2 = 0

Solving
-500 + 260p + p2 = 0

Solving for variable 'p'.

Begin completing the square.

Move the constant term to the right:

Add '500' to each side of the equation.
-500 + 260p + 500 + p2 = 0 + 500

Reorder the terms:
-500 + 500 + 260p + p2 = 0 + 500

Combine like terms: -500 + 500 = 0
0 + 260p + p2 = 0 + 500
260p + p2 = 0 + 500

Combine like terms: 0 + 500 = 500
260p + p2 = 500

The p term is 260p.  Take half its coefficient (130).
Square it (16900) and add it to both sides.

Add '16900' to each side of the equation.
260p + 16900 + p2 = 500 + 16900

Reorder the terms:
16900 + 260p + p2 = 500 + 16900

Combine like terms: 500 + 16900 = 17400
16900 + 260p + p2 = 17400

Factor a perfect square on the left side:
(p + 130)(p + 130) = 17400

Calculate the square root of the right side: 131.909059583

Break this problem into two subproblems by setting 
(p + 130) equal to 131.909059583 and -131.909059583.


Subproblem 1
p + 130 = 131.909059583

Simplifying
p + 130 = 131.909059583

Reorder the terms:
130 + p = 131.909059583

Solving
130 + p = 131.909059583

Solving for variable 'p'.

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

Add '-130' to each side of the equation.
130 + -130 + p = 131.909059583 + -130

Combine like terms: 130 + -130 = 0
0 + p = 131.909059583 + -130
p = 131.909059583 + -130

Combine like terms: 131.909059583 + -130 = 1.909059583
p = 1.909059583

Simplifying
p = 1.909059583


Subproblem 2
p + 130 = -131.909059583

Simplifying
p + 130 = -131.909059583

Reorder the terms:
130 + p = -131.909059583

Solving
130 + p = -131.909059583

Solving for variable 'p'.

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

Add '-130' to each side of the equation.
130 + -130 + p = -131.909059583 + -130

Combine like terms: 130 + -130 = 0
0 + p = -131.909059583 + -130
p = -131.909059583 + -130

Combine like terms: -131.909059583 + -130 = -261.909059583
p = -261.909059583

Simplifying
p = -261.909059583


Solution
The solution to the problem is based on the solutions
from the subproblems.
p = {1.909059583, -261.909059583}

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