2p^2-16p-10=0

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Solution for 2p^2-16p-10=0 equation: 


Simplifying
2p2 + -16p + -10 = 0

Reorder the terms:
-10 + -16p + 2p2 = 0

Solving
-10 + -16p + 2p2 = 0

Solving for variable 'p'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-5 + -8p + p2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-5 + -8p + p2)' equal to zero and attempt to solve:

Simplifying
-5 + -8p + p2 = 0

Solving
-5 + -8p + p2 = 0

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 = 8.582575695
p = 8.582575695

Simplifying
p = 8.582575695


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 = -0.582575695
p = -0.582575695

Simplifying
p = -0.582575695


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

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