p^2-8p-51=0

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Solution for p^2-8p-51=0 equation: 


Simplifying
p2 + -8p + -51 = 0

Reorder the terms:
-51 + -8p + p2 = 0

Solving
-51 + -8p + p2 = 0

Solving for variable 'p'.

Begin completing the square.

Move the constant term to the right:

Add '51' to each side of the equation.
-51 + -8p + 51 + p2 = 0 + 51

Reorder the terms:
-51 + 51 + -8p + p2 = 0 + 51

Combine like terms: -51 + 51 = 0
0 + -8p + p2 = 0 + 51
-8p + p2 = 0 + 51

Combine like terms: 0 + 51 = 51
-8p + p2 = 51

The p term is -8p.  Take half its coefficient (-4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
-8p + 16 + p2 = 51 + 16

Reorder the terms:
16 + -8p + p2 = 51 + 16

Combine like terms: 51 + 16 = 67
16 + -8p + p2 = 67

Factor a perfect square on the left side:
(p + -4)(p + -4) = 67

Calculate the square root of the right side: 8.185352772

Break this problem into two subproblems by setting 
(p + -4) equal to 8.185352772 and -8.185352772.


Subproblem 1
p + -4 = 8.185352772

Simplifying
p + -4 = 8.185352772

Reorder the terms:
-4 + p = 8.185352772

Solving
-4 + p = 8.185352772

Solving for variable 'p'.

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

Add '4' to each side of the equation.
-4 + 4 + p = 8.185352772 + 4

Combine like terms: -4 + 4 = 0
0 + p = 8.185352772 + 4
p = 8.185352772 + 4

Combine like terms: 8.185352772 + 4 = 12.185352772
p = 12.185352772

Simplifying
p = 12.185352772


Subproblem 2
p + -4 = -8.185352772

Simplifying
p + -4 = -8.185352772

Reorder the terms:
-4 + p = -8.185352772

Solving
-4 + p = -8.185352772

Solving for variable 'p'.

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

Add '4' to each side of the equation.
-4 + 4 + p = -8.185352772 + 4

Combine like terms: -4 + 4 = 0
0 + p = -8.185352772 + 4
p = -8.185352772 + 4

Combine like terms: -8.185352772 + 4 = -4.185352772
p = -4.185352772

Simplifying
p = -4.185352772


Solution
The solution to the problem is based on the solutions
from the subproblems.
p = {12.185352772, -4.185352772}

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