p^2+8p-5=0

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Solution for p^2+8p-5=0 equation: 


Simplifying
p2 + 8p + -5 = 0

Reorder the terms:
-5 + 8p + p2 = 0

Solving
-5 + 8p + p2 = 0

Solving for variable 'p'.

Begin completing the square.

Move the constant term to the right:

Add '5' to each side of the equation.
-5 + 8p + 5 + p2 = 0 + 5

Reorder the terms:
-5 + 5 + 8p + p2 = 0 + 5

Combine like terms: -5 + 5 = 0
0 + 8p + p2 = 0 + 5
8p + p2 = 0 + 5

Combine like terms: 0 + 5 = 5
8p + p2 = 5

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 = 5 + 16

Reorder the terms:
16 + 8p + p2 = 5 + 16

Combine like terms: 5 + 16 = 21
16 + 8p + p2 = 21

Factor a perfect square on the left side:
(p + 4)(p + 4) = 21

Calculate the square root of the right side: 4.582575695

Break this problem into two subproblems by setting 
(p + 4) equal to 4.582575695 and -4.582575695.


Subproblem 1
p + 4 = 4.582575695

Simplifying
p + 4 = 4.582575695

Reorder the terms:
4 + p = 4.582575695

Solving
4 + p = 4.582575695

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 = 4.582575695 + -4

Combine like terms: 4 + -4 = 0
0 + p = 4.582575695 + -4
p = 4.582575695 + -4

Combine like terms: 4.582575695 + -4 = 0.582575695
p = 0.582575695

Simplifying
p = 0.582575695


Subproblem 2
p + 4 = -4.582575695

Simplifying
p + 4 = -4.582575695

Reorder the terms:
4 + p = -4.582575695

Solving
4 + p = -4.582575695

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 = -4.582575695 + -4

Combine like terms: 4 + -4 = 0
0 + p = -4.582575695 + -4
p = -4.582575695 + -4

Combine like terms: -4.582575695 + -4 = -8.582575695
p = -8.582575695

Simplifying
p = -8.582575695


Solution
The solution to the problem is based on the solutions
from the subproblems.
p = {0.582575695, -8.582575695}

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