p^2+16p-8=0

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Solution for p^2+16p-8=0 equation: 


Simplifying
p2 + 16p + -8 = 0

Reorder the terms:
-8 + 16p + p2 = 0

Solving
-8 + 16p + 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 + 16p + 8 + p2 = 0 + 8

Reorder the terms:
-8 + 8 + 16p + p2 = 0 + 8

Combine like terms: -8 + 8 = 0
0 + 16p + p2 = 0 + 8
16p + p2 = 0 + 8

Combine like terms: 0 + 8 = 8
16p + p2 = 8

The p term is 16p.  Take half its coefficient (8).
Square it (64) and add it to both sides.

Add '64' to each side of the equation.
16p + 64 + p2 = 8 + 64

Reorder the terms:
64 + 16p + p2 = 8 + 64

Combine like terms: 8 + 64 = 72
64 + 16p + p2 = 72

Factor a perfect square on the left side:
(p + 8)(p + 8) = 72

Calculate the square root of the right side: 8.485281374

Break this problem into two subproblems by setting 
(p + 8) equal to 8.485281374 and -8.485281374.


Subproblem 1
p + 8 = 8.485281374

Simplifying
p + 8 = 8.485281374

Reorder the terms:
8 + p = 8.485281374

Solving
8 + p = 8.485281374

Solving for variable 'p'.

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

Add '-8' to each side of the equation.
8 + -8 + p = 8.485281374 + -8

Combine like terms: 8 + -8 = 0
0 + p = 8.485281374 + -8
p = 8.485281374 + -8

Combine like terms: 8.485281374 + -8 = 0.485281374
p = 0.485281374

Simplifying
p = 0.485281374


Subproblem 2
p + 8 = -8.485281374

Simplifying
p + 8 = -8.485281374

Reorder the terms:
8 + p = -8.485281374

Solving
8 + p = -8.485281374

Solving for variable 'p'.

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

Add '-8' to each side of the equation.
8 + -8 + p = -8.485281374 + -8

Combine like terms: 8 + -8 = 0
0 + p = -8.485281374 + -8
p = -8.485281374 + -8

Combine like terms: -8.485281374 + -8 = -16.485281374
p = -16.485281374

Simplifying
p = -16.485281374


Solution
The solution to the problem is based on the solutions
from the subproblems.
p = {0.485281374, -16.485281374}

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