p^2-8p-58=0

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Solution for p^2-8p-58=0 equation: 


Simplifying
p2 + -8p + -58 = 0

Reorder the terms:
-58 + -8p + p2 = 0

Solving
-58 + -8p + p2 = 0

Solving for variable 'p'.

Begin completing the square.

Move the constant term to the right:

Add '58' to each side of the equation.
-58 + -8p + 58 + p2 = 0 + 58

Reorder the terms:
-58 + 58 + -8p + p2 = 0 + 58

Combine like terms: -58 + 58 = 0
0 + -8p + p2 = 0 + 58
-8p + p2 = 0 + 58

Combine like terms: 0 + 58 = 58
-8p + p2 = 58

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 = 58 + 16

Reorder the terms:
16 + -8p + p2 = 58 + 16

Combine like terms: 58 + 16 = 74
16 + -8p + p2 = 74

Factor a perfect square on the left side:
(p + -4)(p + -4) = 74

Calculate the square root of the right side: 8.602325267

Break this problem into two subproblems by setting 
(p + -4) equal to 8.602325267 and -8.602325267.


Subproblem 1
p + -4 = 8.602325267

Simplifying
p + -4 = 8.602325267

Reorder the terms:
-4 + p = 8.602325267

Solving
-4 + p = 8.602325267

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 = 8.602325267 + 4

Combine like terms: -4 + 4 = 0
0 + p = 8.602325267 + 4
p = 8.602325267 + 4

Combine like terms: 8.602325267 + 4 = 12.602325267
p = 12.602325267

Simplifying
p = 12.602325267


Subproblem 2
p + -4 = -8.602325267

Simplifying
p + -4 = -8.602325267

Reorder the terms:
-4 + p = -8.602325267

Solving
-4 + p = -8.602325267

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 = -8.602325267 + 4

Combine like terms: -4 + 4 = 0
0 + p = -8.602325267 + 4
p = -8.602325267 + 4

Combine like terms: -8.602325267 + 4 = -4.602325267
p = -4.602325267

Simplifying
p = -4.602325267


Solution
The solution to the problem is based on the solutions
from the subproblems.
p = {12.602325267, -4.602325267}

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