-2p(p-13)=-8

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Solution for -2p(p-13)=-8 equation: 


Simplifying
-2p(p + -13) = -8

Reorder the terms:
-2p(-13 + p) = -8
(-13 * -2p + p * -2p) = -8
(26p + -2p2) = -8

Solving
26p + -2p2 = -8

Solving for variable 'p'.

Reorder the terms:
8 + 26p + -2p2 = -8 + 8

Combine like terms: -8 + 8 = 0
8 + 26p + -2p2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(4 + 13p + -1p2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(4 + 13p + -1p2)' equal to zero and attempt to solve:

Simplifying
4 + 13p + -1p2 = 0

Solving
4 + 13p + -1p2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-4 + -13p + p2 = 0

Move the constant term to the right:

Add '4' to each side of the equation.
-4 + -13p + 4 + p2 = 0 + 4

Reorder the terms:
-4 + 4 + -13p + p2 = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -13p + p2 = 0 + 4
-13p + p2 = 0 + 4

Combine like terms: 0 + 4 = 4
-13p + p2 = 4

The p term is -13p.  Take half its coefficient (-6.5).
Square it (42.25) and add it to both sides.

Add '42.25' to each side of the equation.
-13p + 42.25 + p2 = 4 + 42.25

Reorder the terms:
42.25 + -13p + p2 = 4 + 42.25

Combine like terms: 4 + 42.25 = 46.25
42.25 + -13p + p2 = 46.25

Factor a perfect square on the left side:
(p + -6.5)(p + -6.5) = 46.25

Calculate the square root of the right side: 6.800735254

Break this problem into two subproblems by setting 
(p + -6.5) equal to 6.800735254 and -6.800735254.


Subproblem 1
p + -6.5 = 6.800735254

Simplifying
p + -6.5 = 6.800735254

Reorder the terms:
-6.5 + p = 6.800735254

Solving
-6.5 + p = 6.800735254

Solving for variable 'p'.

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

Add '6.5' to each side of the equation.
-6.5 + 6.5 + p = 6.800735254 + 6.5

Combine like terms: -6.5 + 6.5 = 0.0
0.0 + p = 6.800735254 + 6.5
p = 6.800735254 + 6.5

Combine like terms: 6.800735254 + 6.5 = 13.300735254
p = 13.300735254

Simplifying
p = 13.300735254


Subproblem 2
p + -6.5 = -6.800735254

Simplifying
p + -6.5 = -6.800735254

Reorder the terms:
-6.5 + p = -6.800735254

Solving
-6.5 + p = -6.800735254

Solving for variable 'p'.

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

Add '6.5' to each side of the equation.
-6.5 + 6.5 + p = -6.800735254 + 6.5

Combine like terms: -6.5 + 6.5 = 0.0
0.0 + p = -6.800735254 + 6.5
p = -6.800735254 + 6.5

Combine like terms: -6.800735254 + 6.5 = -0.300735254
p = -0.300735254

Simplifying
p = -0.300735254


Solution
The solution to the problem is based on the solutions
from the subproblems.
p = {13.300735254, -0.300735254}
Solution
p = {13.300735254, -0.300735254}

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