3p^2-3p-8=0

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Solution for 3p^2-3p-8=0 equation: 


Simplifying
3p2 + -3p + -8 = 0

Reorder the terms:
-8 + -3p + 3p2 = 0

Solving
-8 + -3p + 3p2 = 0

Solving for variable 'p'.

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

Divide each side by '3'.
-2.666666667 + -1p + p2 = 0

Move the constant term to the right:

Add '2.666666667' to each side of the equation.
-2.666666667 + -1p + 2.666666667 + p2 = 0 + 2.666666667

Reorder the terms:
-2.666666667 + 2.666666667 + -1p + p2 = 0 + 2.666666667

Combine like terms: -2.666666667 + 2.666666667 = 0.000000000
0.000000000 + -1p + p2 = 0 + 2.666666667
-1p + p2 = 0 + 2.666666667

Combine like terms: 0 + 2.666666667 = 2.666666667
-1p + p2 = 2.666666667

The p term is -1p.  Take half its coefficient (-0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-1p + 0.25 + p2 = 2.666666667 + 0.25

Reorder the terms:
0.25 + -1p + p2 = 2.666666667 + 0.25

Combine like terms: 2.666666667 + 0.25 = 2.916666667
0.25 + -1p + p2 = 2.916666667

Factor a perfect square on the left side:
(p + -0.5)(p + -0.5) = 2.916666667

Calculate the square root of the right side: 1.707825128

Break this problem into two subproblems by setting 
(p + -0.5) equal to 1.707825128 and -1.707825128.


Subproblem 1
p + -0.5 = 1.707825128

Simplifying
p + -0.5 = 1.707825128

Reorder the terms:
-0.5 + p = 1.707825128

Solving
-0.5 + p = 1.707825128

Solving for variable 'p'.

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

Add '0.5' to each side of the equation.
-0.5 + 0.5 + p = 1.707825128 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + p = 1.707825128 + 0.5
p = 1.707825128 + 0.5

Combine like terms: 1.707825128 + 0.5 = 2.207825128
p = 2.207825128

Simplifying
p = 2.207825128


Subproblem 2
p + -0.5 = -1.707825128

Simplifying
p + -0.5 = -1.707825128

Reorder the terms:
-0.5 + p = -1.707825128

Solving
-0.5 + p = -1.707825128

Solving for variable 'p'.

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

Add '0.5' to each side of the equation.
-0.5 + 0.5 + p = -1.707825128 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + p = -1.707825128 + 0.5
p = -1.707825128 + 0.5

Combine like terms: -1.707825128 + 0.5 = -1.207825128
p = -1.207825128

Simplifying
p = -1.207825128


Solution
The solution to the problem is based on the solutions
from the subproblems.
p = {2.207825128, -1.207825128}

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