3p^2+12p-2=0

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Solution for 3p^2+12p-2=0 equation: 


Simplifying
3p2 + 12p + -2 = 0

Reorder the terms:
-2 + 12p + 3p2 = 0

Solving
-2 + 12p + 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'.
-0.6666666667 + 4p + p2 = 0

Move the constant term to the right:

Add '0.6666666667' to each side of the equation.
-0.6666666667 + 4p + 0.6666666667 + p2 = 0 + 0.6666666667

Reorder the terms:
-0.6666666667 + 0.6666666667 + 4p + p2 = 0 + 0.6666666667

Combine like terms: -0.6666666667 + 0.6666666667 = 0.0000000000
0.0000000000 + 4p + p2 = 0 + 0.6666666667
4p + p2 = 0 + 0.6666666667

Combine like terms: 0 + 0.6666666667 = 0.6666666667
4p + p2 = 0.6666666667

The p term is 4p.  Take half its coefficient (2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
4p + 4 + p2 = 0.6666666667 + 4

Reorder the terms:
4 + 4p + p2 = 0.6666666667 + 4

Combine like terms: 0.6666666667 + 4 = 4.6666666667
4 + 4p + p2 = 4.6666666667

Factor a perfect square on the left side:
(p + 2)(p + 2) = 4.6666666667

Calculate the square root of the right side: 2.160246899

Break this problem into two subproblems by setting 
(p + 2) equal to 2.160246899 and -2.160246899.


Subproblem 1
p + 2 = 2.160246899

Simplifying
p + 2 = 2.160246899

Reorder the terms:
2 + p = 2.160246899

Solving
2 + p = 2.160246899

Solving for variable 'p'.

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

Add '-2' to each side of the equation.
2 + -2 + p = 2.160246899 + -2

Combine like terms: 2 + -2 = 0
0 + p = 2.160246899 + -2
p = 2.160246899 + -2

Combine like terms: 2.160246899 + -2 = 0.160246899
p = 0.160246899

Simplifying
p = 0.160246899


Subproblem 2
p + 2 = -2.160246899

Simplifying
p + 2 = -2.160246899

Reorder the terms:
2 + p = -2.160246899

Solving
2 + p = -2.160246899

Solving for variable 'p'.

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

Add '-2' to each side of the equation.
2 + -2 + p = -2.160246899 + -2

Combine like terms: 2 + -2 = 0
0 + p = -2.160246899 + -2
p = -2.160246899 + -2

Combine like terms: -2.160246899 + -2 = -4.160246899
p = -4.160246899

Simplifying
p = -4.160246899


Solution
The solution to the problem is based on the solutions
from the subproblems.
p = {0.160246899, -4.160246899}

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