3p^2-4p-9=0

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Solution for 3p^2-4p-9=0 equation: 


Simplifying
3p2 + -4p + -9 = 0

Reorder the terms:
-9 + -4p + 3p2 = 0

Solving
-9 + -4p + 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'.
-3 + -1.333333333p + p2 = 0

Move the constant term to the right:

Add '3' to each side of the equation.
-3 + -1.333333333p + 3 + p2 = 0 + 3

Reorder the terms:
-3 + 3 + -1.333333333p + p2 = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1.333333333p + p2 = 0 + 3
-1.333333333p + p2 = 0 + 3

Combine like terms: 0 + 3 = 3
-1.333333333p + p2 = 3

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 = 3 + 0.4444444442

Reorder the terms:
0.4444444442 + -1.333333333p + p2 = 3 + 0.4444444442

Combine like terms: 3 + 0.4444444442 = 3.4444444442
0.4444444442 + -1.333333333p + p2 = 3.4444444442

Factor a perfect square on the left side:
(p + -0.6666666665)(p + -0.6666666665) = 3.4444444442

Calculate the square root of the right side: 1.855921454

Break this problem into two subproblems by setting 
(p + -0.6666666665) equal to 1.855921454 and -1.855921454.


Subproblem 1
p + -0.6666666665 = 1.855921454

Simplifying
p + -0.6666666665 = 1.855921454

Reorder the terms:
-0.6666666665 + p = 1.855921454

Solving
-0.6666666665 + p = 1.855921454

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 = 1.855921454 + 0.6666666665

Combine like terms: -0.6666666665 + 0.6666666665 = 0.0000000000
0.0000000000 + p = 1.855921454 + 0.6666666665
p = 1.855921454 + 0.6666666665

Combine like terms: 1.855921454 + 0.6666666665 = 2.5225881205
p = 2.5225881205

Simplifying
p = 2.5225881205


Subproblem 2
p + -0.6666666665 = -1.855921454

Simplifying
p + -0.6666666665 = -1.855921454

Reorder the terms:
-0.6666666665 + p = -1.855921454

Solving
-0.6666666665 + p = -1.855921454

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 = -1.855921454 + 0.6666666665

Combine like terms: -0.6666666665 + 0.6666666665 = 0.0000000000
0.0000000000 + p = -1.855921454 + 0.6666666665
p = -1.855921454 + 0.6666666665

Combine like terms: -1.855921454 + 0.6666666665 = -1.1892547875
p = -1.1892547875

Simplifying
p = -1.1892547875


Solution
The solution to the problem is based on the solutions
from the subproblems.
p = {2.5225881205, -1.1892547875}

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