p^2-14p-8=0

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Solution for p^2-14p-8=0 equation: 


Simplifying
p2 + -14p + -8 = 0

Reorder the terms:
-8 + -14p + p2 = 0

Solving
-8 + -14p + p2 = 0

Solving for variable 'p'.

Begin completing the square.

Move the constant term to the right:

Add '8' to each side of the equation.
-8 + -14p + 8 + p2 = 0 + 8

Reorder the terms:
-8 + 8 + -14p + p2 = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -14p + p2 = 0 + 8
-14p + p2 = 0 + 8

Combine like terms: 0 + 8 = 8
-14p + p2 = 8

The p term is -14p.  Take half its coefficient (-7).
Square it (49) and add it to both sides.

Add '49' to each side of the equation.
-14p + 49 + p2 = 8 + 49

Reorder the terms:
49 + -14p + p2 = 8 + 49

Combine like terms: 8 + 49 = 57
49 + -14p + p2 = 57

Factor a perfect square on the left side:
(p + -7)(p + -7) = 57

Calculate the square root of the right side: 7.549834435

Break this problem into two subproblems by setting 
(p + -7) equal to 7.549834435 and -7.549834435.


Subproblem 1
p + -7 = 7.549834435

Simplifying
p + -7 = 7.549834435

Reorder the terms:
-7 + p = 7.549834435

Solving
-7 + p = 7.549834435

Solving for variable 'p'.

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

Add '7' to each side of the equation.
-7 + 7 + p = 7.549834435 + 7

Combine like terms: -7 + 7 = 0
0 + p = 7.549834435 + 7
p = 7.549834435 + 7

Combine like terms: 7.549834435 + 7 = 14.549834435
p = 14.549834435

Simplifying
p = 14.549834435


Subproblem 2
p + -7 = -7.549834435

Simplifying
p + -7 = -7.549834435

Reorder the terms:
-7 + p = -7.549834435

Solving
-7 + p = -7.549834435

Solving for variable 'p'.

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

Add '7' to each side of the equation.
-7 + 7 + p = -7.549834435 + 7

Combine like terms: -7 + 7 = 0
0 + p = -7.549834435 + 7
p = -7.549834435 + 7

Combine like terms: -7.549834435 + 7 = -0.549834435
p = -0.549834435

Simplifying
p = -0.549834435


Solution
The solution to the problem is based on the solutions
from the subproblems.
p = {14.549834435, -0.549834435}

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