-6x^2+56x-9=0

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Solution for -6x^2+56x-9=0 equation: 


Simplifying
-6x2 + 56x + -9 = 0

Reorder the terms:
-9 + 56x + -6x2 = 0

Solving
-9 + 56x + -6x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-6 the coefficient of the squared term: 

Divide each side by '-6'.
1.5 + -9.333333333x + x2 = 0

Move the constant term to the right:

Add '-1.5' to each side of the equation.
1.5 + -9.333333333x + -1.5 + x2 = 0 + -1.5

Reorder the terms:
1.5 + -1.5 + -9.333333333x + x2 = 0 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + -9.333333333x + x2 = 0 + -1.5
-9.333333333x + x2 = 0 + -1.5

Combine like terms: 0 + -1.5 = -1.5
-9.333333333x + x2 = -1.5

The x term is -9.333333333x.  Take half its coefficient (-4.666666667).
Square it (21.77777778) and add it to both sides.

Add '21.77777778' to each side of the equation.
-9.333333333x + 21.77777778 + x2 = -1.5 + 21.77777778

Reorder the terms:
21.77777778 + -9.333333333x + x2 = -1.5 + 21.77777778

Combine like terms: -1.5 + 21.77777778 = 20.27777778
21.77777778 + -9.333333333x + x2 = 20.27777778

Factor a perfect square on the left side:
(x + -4.666666667)(x + -4.666666667) = 20.27777778

Calculate the square root of the right side: 4.503085362

Break this problem into two subproblems by setting 
(x + -4.666666667) equal to 4.503085362 and -4.503085362.


Subproblem 1
x + -4.666666667 = 4.503085362

Simplifying
x + -4.666666667 = 4.503085362

Reorder the terms:
-4.666666667 + x = 4.503085362

Solving
-4.666666667 + x = 4.503085362

Solving for variable 'x'.

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

Add '4.666666667' to each side of the equation.
-4.666666667 + 4.666666667 + x = 4.503085362 + 4.666666667

Combine like terms: -4.666666667 + 4.666666667 = 0.000000000
0.000000000 + x = 4.503085362 + 4.666666667
x = 4.503085362 + 4.666666667

Combine like terms: 4.503085362 + 4.666666667 = 9.169752029
x = 9.169752029

Simplifying
x = 9.169752029


Subproblem 2
x + -4.666666667 = -4.503085362

Simplifying
x + -4.666666667 = -4.503085362

Reorder the terms:
-4.666666667 + x = -4.503085362

Solving
-4.666666667 + x = -4.503085362

Solving for variable 'x'.

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

Add '4.666666667' to each side of the equation.
-4.666666667 + 4.666666667 + x = -4.503085362 + 4.666666667

Combine like terms: -4.666666667 + 4.666666667 = 0.000000000
0.000000000 + x = -4.503085362 + 4.666666667
x = -4.503085362 + 4.666666667

Combine like terms: -4.503085362 + 4.666666667 = 0.163581305
x = 0.163581305

Simplifying
x = 0.163581305


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {9.169752029, 0.163581305}

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