3p^2-p-6=0

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


Simplifying
3p2 + -1p + -6 = 0

Reorder the terms:
-6 + -1p + 3p2 = 0

Solving
-6 + -1p + 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 + -0.3333333333p + p2 = 0

Move the constant term to the right:

Add '2' to each side of the equation.
-2 + -0.3333333333p + 2 + p2 = 0 + 2

Reorder the terms:
-2 + 2 + -0.3333333333p + p2 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -0.3333333333p + p2 = 0 + 2
-0.3333333333p + p2 = 0 + 2

Combine like terms: 0 + 2 = 2
-0.3333333333p + p2 = 2

The p term is -0.3333333333p.  Take half its coefficient (-0.1666666667).
Square it (0.02777777779) and add it to both sides.

Add '0.02777777779' to each side of the equation.
-0.3333333333p + 0.02777777779 + p2 = 2 + 0.02777777779

Reorder the terms:
0.02777777779 + -0.3333333333p + p2 = 2 + 0.02777777779

Combine like terms: 2 + 0.02777777779 = 2.02777777779
0.02777777779 + -0.3333333333p + p2 = 2.02777777779

Factor a perfect square on the left side:
(p + -0.1666666667)(p + -0.1666666667) = 2.02777777779

Calculate the square root of the right side: 1.424000624

Break this problem into two subproblems by setting 
(p + -0.1666666667) equal to 1.424000624 and -1.424000624.


Subproblem 1
p + -0.1666666667 = 1.424000624

Simplifying
p + -0.1666666667 = 1.424000624

Reorder the terms:
-0.1666666667 + p = 1.424000624

Solving
-0.1666666667 + p = 1.424000624

Solving for variable 'p'.

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

Add '0.1666666667' to each side of the equation.
-0.1666666667 + 0.1666666667 + p = 1.424000624 + 0.1666666667

Combine like terms: -0.1666666667 + 0.1666666667 = 0.0000000000
0.0000000000 + p = 1.424000624 + 0.1666666667
p = 1.424000624 + 0.1666666667

Combine like terms: 1.424000624 + 0.1666666667 = 1.5906672907
p = 1.5906672907

Simplifying
p = 1.5906672907


Subproblem 2
p + -0.1666666667 = -1.424000624

Simplifying
p + -0.1666666667 = -1.424000624

Reorder the terms:
-0.1666666667 + p = -1.424000624

Solving
-0.1666666667 + p = -1.424000624

Solving for variable 'p'.

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

Add '0.1666666667' to each side of the equation.
-0.1666666667 + 0.1666666667 + p = -1.424000624 + 0.1666666667

Combine like terms: -0.1666666667 + 0.1666666667 = 0.0000000000
0.0000000000 + p = -1.424000624 + 0.1666666667
p = -1.424000624 + 0.1666666667

Combine like terms: -1.424000624 + 0.1666666667 = -1.2573339573
p = -1.2573339573

Simplifying
p = -1.2573339573


Solution
The solution to the problem is based on the solutions
from the subproblems.
p = {1.5906672907, -1.2573339573}

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