-6p^2-2p+9=0

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


Simplifying
-6p2 + -2p + 9 = 0

Reorder the terms:
9 + -2p + -6p2 = 0

Solving
9 + -2p + -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 + 0.3333333333p + p2 = 0

Move the constant term to the right:

Add '1.5' to each side of the equation.
-1.5 + 0.3333333333p + 1.5 + p2 = 0 + 1.5

Reorder the terms:
-1.5 + 1.5 + 0.3333333333p + p2 = 0 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + 0.3333333333p + p2 = 0 + 1.5
0.3333333333p + p2 = 0 + 1.5

Combine like terms: 0 + 1.5 = 1.5
0.3333333333p + p2 = 1.5

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 = 1.5 + 0.02777777779

Reorder the terms:
0.02777777779 + 0.3333333333p + p2 = 1.5 + 0.02777777779

Combine like terms: 1.5 + 0.02777777779 = 1.52777777779
0.02777777779 + 0.3333333333p + p2 = 1.52777777779

Factor a perfect square on the left side:
(p + 0.1666666667)(p + 0.1666666667) = 1.52777777779

Calculate the square root of the right side: 1.236033081

Break this problem into two subproblems by setting 
(p + 0.1666666667) equal to 1.236033081 and -1.236033081.


Subproblem 1
p + 0.1666666667 = 1.236033081

Simplifying
p + 0.1666666667 = 1.236033081

Reorder the terms:
0.1666666667 + p = 1.236033081

Solving
0.1666666667 + p = 1.236033081

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 = 1.236033081 + -0.1666666667

Combine like terms: 0.1666666667 + -0.1666666667 = 0.0000000000
0.0000000000 + p = 1.236033081 + -0.1666666667
p = 1.236033081 + -0.1666666667

Combine like terms: 1.236033081 + -0.1666666667 = 1.0693664143
p = 1.0693664143

Simplifying
p = 1.0693664143


Subproblem 2
p + 0.1666666667 = -1.236033081

Simplifying
p + 0.1666666667 = -1.236033081

Reorder the terms:
0.1666666667 + p = -1.236033081

Solving
0.1666666667 + p = -1.236033081

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 = -1.236033081 + -0.1666666667

Combine like terms: 0.1666666667 + -0.1666666667 = 0.0000000000
0.0000000000 + p = -1.236033081 + -0.1666666667
p = -1.236033081 + -0.1666666667

Combine like terms: -1.236033081 + -0.1666666667 = -1.4026997477
p = -1.4026997477

Simplifying
p = -1.4026997477


Solution
The solution to the problem is based on the solutions
from the subproblems.
p = {1.0693664143, -1.4026997477}

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