6p^2-p-9=0

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Solution for 6p^2-p-9=0 equation: 


Simplifying
6p2 + -1p + -9 = 0

Reorder the terms:
-9 + -1p + 6p2 = 0

Solving
-9 + -1p + 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'.
-1.5 + -0.1666666667p + p2 = 0

Move the constant term to the right:

Add '1.5' to each side of the equation.
-1.5 + -0.1666666667p + 1.5 + p2 = 0 + 1.5

Reorder the terms:
-1.5 + 1.5 + -0.1666666667p + p2 = 0 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + -0.1666666667p + p2 = 0 + 1.5
-0.1666666667p + p2 = 0 + 1.5

Combine like terms: 0 + 1.5 = 1.5
-0.1666666667p + p2 = 1.5

The p term is -0.1666666667p.  Take half its coefficient (-0.08333333335).
Square it (0.006944444447) and add it to both sides.

Add '0.006944444447' to each side of the equation.
-0.1666666667p + 0.006944444447 + p2 = 1.5 + 0.006944444447

Reorder the terms:
0.006944444447 + -0.1666666667p + p2 = 1.5 + 0.006944444447

Combine like terms: 1.5 + 0.006944444447 = 1.506944444447
0.006944444447 + -0.1666666667p + p2 = 1.506944444447

Factor a perfect square on the left side:
(p + -0.08333333335)(p + -0.08333333335) = 1.506944444447

Calculate the square root of the right side: 1.227576655

Break this problem into two subproblems by setting 
(p + -0.08333333335) equal to 1.227576655 and -1.227576655.


Subproblem 1
p + -0.08333333335 = 1.227576655

Simplifying
p + -0.08333333335 = 1.227576655

Reorder the terms:
-0.08333333335 + p = 1.227576655

Solving
-0.08333333335 + p = 1.227576655

Solving for variable 'p'.

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

Add '0.08333333335' to each side of the equation.
-0.08333333335 + 0.08333333335 + p = 1.227576655 + 0.08333333335

Combine like terms: -0.08333333335 + 0.08333333335 = 0.00000000000
0.00000000000 + p = 1.227576655 + 0.08333333335
p = 1.227576655 + 0.08333333335

Combine like terms: 1.227576655 + 0.08333333335 = 1.31090998835
p = 1.31090998835

Simplifying
p = 1.31090998835


Subproblem 2
p + -0.08333333335 = -1.227576655

Simplifying
p + -0.08333333335 = -1.227576655

Reorder the terms:
-0.08333333335 + p = -1.227576655

Solving
-0.08333333335 + p = -1.227576655

Solving for variable 'p'.

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

Add '0.08333333335' to each side of the equation.
-0.08333333335 + 0.08333333335 + p = -1.227576655 + 0.08333333335

Combine like terms: -0.08333333335 + 0.08333333335 = 0.00000000000
0.00000000000 + p = -1.227576655 + 0.08333333335
p = -1.227576655 + 0.08333333335

Combine like terms: -1.227576655 + 0.08333333335 = -1.14424332165
p = -1.14424332165

Simplifying
p = -1.14424332165


Solution
The solution to the problem is based on the solutions
from the subproblems.
p = {1.31090998835, -1.14424332165}

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