p^2-5p-25=0

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Solution for p^2-5p-25=0 equation: 


Simplifying
p2 + -5p + -25 = 0

Reorder the terms:
-25 + -5p + p2 = 0

Solving
-25 + -5p + p2 = 0

Solving for variable 'p'.

Begin completing the square.

Move the constant term to the right:

Add '25' to each side of the equation.
-25 + -5p + 25 + p2 = 0 + 25

Reorder the terms:
-25 + 25 + -5p + p2 = 0 + 25

Combine like terms: -25 + 25 = 0
0 + -5p + p2 = 0 + 25
-5p + p2 = 0 + 25

Combine like terms: 0 + 25 = 25
-5p + p2 = 25

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 = 25 + 6.25

Reorder the terms:
6.25 + -5p + p2 = 25 + 6.25

Combine like terms: 25 + 6.25 = 31.25
6.25 + -5p + p2 = 31.25

Factor a perfect square on the left side:
(p + -2.5)(p + -2.5) = 31.25

Calculate the square root of the right side: 5.590169944

Break this problem into two subproblems by setting 
(p + -2.5) equal to 5.590169944 and -5.590169944.


Subproblem 1
p + -2.5 = 5.590169944

Simplifying
p + -2.5 = 5.590169944

Reorder the terms:
-2.5 + p = 5.590169944

Solving
-2.5 + p = 5.590169944

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 = 5.590169944 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + p = 5.590169944 + 2.5
p = 5.590169944 + 2.5

Combine like terms: 5.590169944 + 2.5 = 8.090169944
p = 8.090169944

Simplifying
p = 8.090169944


Subproblem 2
p + -2.5 = -5.590169944

Simplifying
p + -2.5 = -5.590169944

Reorder the terms:
-2.5 + p = -5.590169944

Solving
-2.5 + p = -5.590169944

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 = -5.590169944 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + p = -5.590169944 + 2.5
p = -5.590169944 + 2.5

Combine like terms: -5.590169944 + 2.5 = -3.090169944
p = -3.090169944

Simplifying
p = -3.090169944


Solution
The solution to the problem is based on the solutions
from the subproblems.
p = {8.090169944, -3.090169944}

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