2p^2-16p-8=0

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


Simplifying
2p2 + -16p + -8 = 0

Reorder the terms:
-8 + -16p + 2p2 = 0

Solving
-8 + -16p + 2p2 = 0

Solving for variable 'p'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-4 + -8p + p2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-4 + -8p + p2)' equal to zero and attempt to solve:

Simplifying
-4 + -8p + p2 = 0

Solving
-4 + -8p + p2 = 0

Begin completing the square.

Move the constant term to the right:

Add '4' to each side of the equation.
-4 + -8p + 4 + p2 = 0 + 4

Reorder the terms:
-4 + 4 + -8p + p2 = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -8p + p2 = 0 + 4
-8p + p2 = 0 + 4

Combine like terms: 0 + 4 = 4
-8p + p2 = 4

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 = 4 + 16

Reorder the terms:
16 + -8p + p2 = 4 + 16

Combine like terms: 4 + 16 = 20
16 + -8p + p2 = 20

Factor a perfect square on the left side:
(p + -4)(p + -4) = 20

Calculate the square root of the right side: 4.472135955

Break this problem into two subproblems by setting 
(p + -4) equal to 4.472135955 and -4.472135955.


Subproblem 1
p + -4 = 4.472135955

Simplifying
p + -4 = 4.472135955

Reorder the terms:
-4 + p = 4.472135955

Solving
-4 + p = 4.472135955

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 = 4.472135955 + 4

Combine like terms: -4 + 4 = 0
0 + p = 4.472135955 + 4
p = 4.472135955 + 4

Combine like terms: 4.472135955 + 4 = 8.472135955
p = 8.472135955

Simplifying
p = 8.472135955


Subproblem 2
p + -4 = -4.472135955

Simplifying
p + -4 = -4.472135955

Reorder the terms:
-4 + p = -4.472135955

Solving
-4 + p = -4.472135955

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 = -4.472135955 + 4

Combine like terms: -4 + 4 = 0
0 + p = -4.472135955 + 4
p = -4.472135955 + 4

Combine like terms: -4.472135955 + 4 = -0.472135955
p = -0.472135955

Simplifying
p = -0.472135955


Solution
The solution to the problem is based on the solutions
from the subproblems.
p = {8.472135955, -0.472135955}
Solution
p = {8.472135955, -0.472135955}

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