6p^2-8p-3=0

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Solution for 6p^2-8p-3=0 equation: 


Simplifying
6p2 + -8p + -3 = 0

Reorder the terms:
-3 + -8p + 6p2 = 0

Solving
-3 + -8p + 6p2 = 0

Solving for variable 'p'.

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

Divide each side by '6'.
-0.5 + -1.333333333p + p2 = 0

Move the constant term to the right:

Add '0.5' to each side of the equation.
-0.5 + -1.333333333p + 0.5 + p2 = 0 + 0.5

Reorder the terms:
-0.5 + 0.5 + -1.333333333p + p2 = 0 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + -1.333333333p + p2 = 0 + 0.5
-1.333333333p + p2 = 0 + 0.5

Combine like terms: 0 + 0.5 = 0.5
-1.333333333p + p2 = 0.5

The p term is -1.333333333p.  Take half its coefficient (-0.6666666665).
Square it (0.4444444442) and add it to both sides.

Add '0.4444444442' to each side of the equation.
-1.333333333p + 0.4444444442 + p2 = 0.5 + 0.4444444442

Reorder the terms:
0.4444444442 + -1.333333333p + p2 = 0.5 + 0.4444444442

Combine like terms: 0.5 + 0.4444444442 = 0.9444444442
0.4444444442 + -1.333333333p + p2 = 0.9444444442

Factor a perfect square on the left side:
(p + -0.6666666665)(p + -0.6666666665) = 0.9444444442

Calculate the square root of the right side: 0.971825316

Break this problem into two subproblems by setting 
(p + -0.6666666665) equal to 0.971825316 and -0.971825316.


Subproblem 1
p + -0.6666666665 = 0.971825316

Simplifying
p + -0.6666666665 = 0.971825316

Reorder the terms:
-0.6666666665 + p = 0.971825316

Solving
-0.6666666665 + p = 0.971825316

Solving for variable 'p'.

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

Add '0.6666666665' to each side of the equation.
-0.6666666665 + 0.6666666665 + p = 0.971825316 + 0.6666666665

Combine like terms: -0.6666666665 + 0.6666666665 = 0.0000000000
0.0000000000 + p = 0.971825316 + 0.6666666665
p = 0.971825316 + 0.6666666665

Combine like terms: 0.971825316 + 0.6666666665 = 1.6384919825
p = 1.6384919825

Simplifying
p = 1.6384919825


Subproblem 2
p + -0.6666666665 = -0.971825316

Simplifying
p + -0.6666666665 = -0.971825316

Reorder the terms:
-0.6666666665 + p = -0.971825316

Solving
-0.6666666665 + p = -0.971825316

Solving for variable 'p'.

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

Add '0.6666666665' to each side of the equation.
-0.6666666665 + 0.6666666665 + p = -0.971825316 + 0.6666666665

Combine like terms: -0.6666666665 + 0.6666666665 = 0.0000000000
0.0000000000 + p = -0.971825316 + 0.6666666665
p = -0.971825316 + 0.6666666665

Combine like terms: -0.971825316 + 0.6666666665 = -0.3051586495
p = -0.3051586495

Simplifying
p = -0.3051586495


Solution
The solution to the problem is based on the solutions
from the subproblems.
p = {1.6384919825, -0.3051586495}

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