8p^2-56p-8=0

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Solution for 8p^2-56p-8=0 equation: 


Simplifying
8p2 + -56p + -8 = 0

Reorder the terms:
-8 + -56p + 8p2 = 0

Solving
-8 + -56p + 8p2 = 0

Solving for variable 'p'.

Factor out the Greatest Common Factor (GCF), '8'.
8(-1 + -7p + p2) = 0

Ignore the factor 8.

Subproblem 1
Set the factor '(-1 + -7p + p2)' equal to zero and attempt to solve:

Simplifying
-1 + -7p + p2 = 0

Solving
-1 + -7p + p2 = 0

Begin completing the square.

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + -7p + 1 + p2 = 0 + 1

Reorder the terms:
-1 + 1 + -7p + p2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -7p + p2 = 0 + 1
-7p + p2 = 0 + 1

Combine like terms: 0 + 1 = 1
-7p + p2 = 1

The p term is -7p.  Take half its coefficient (-3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
-7p + 12.25 + p2 = 1 + 12.25

Reorder the terms:
12.25 + -7p + p2 = 1 + 12.25

Combine like terms: 1 + 12.25 = 13.25
12.25 + -7p + p2 = 13.25

Factor a perfect square on the left side:
(p + -3.5)(p + -3.5) = 13.25

Calculate the square root of the right side: 3.640054945

Break this problem into two subproblems by setting 
(p + -3.5) equal to 3.640054945 and -3.640054945.


Subproblem 1
p + -3.5 = 3.640054945

Simplifying
p + -3.5 = 3.640054945

Reorder the terms:
-3.5 + p = 3.640054945

Solving
-3.5 + p = 3.640054945

Solving for variable 'p'.

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

Add '3.5' to each side of the equation.
-3.5 + 3.5 + p = 3.640054945 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + p = 3.640054945 + 3.5
p = 3.640054945 + 3.5

Combine like terms: 3.640054945 + 3.5 = 7.140054945
p = 7.140054945

Simplifying
p = 7.140054945


Subproblem 2
p + -3.5 = -3.640054945

Simplifying
p + -3.5 = -3.640054945

Reorder the terms:
-3.5 + p = -3.640054945

Solving
-3.5 + p = -3.640054945

Solving for variable 'p'.

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

Add '3.5' to each side of the equation.
-3.5 + 3.5 + p = -3.640054945 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + p = -3.640054945 + 3.5
p = -3.640054945 + 3.5

Combine like terms: -3.640054945 + 3.5 = -0.140054945
p = -0.140054945

Simplifying
p = -0.140054945


Solution
The solution to the problem is based on the solutions
from the subproblems.
p = {7.140054945, -0.140054945}
Solution
p = {7.140054945, -0.140054945}

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