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 = 23.27777778
21.77777778 + 9.333333333x + x2 = 23.27777778

Factor a perfect square on the left side:
(x + 4.666666667)(x + 4.666666667) = 23.27777778

Calculate the square root of the right side: 4.824704942

Break this problem into two subproblems by setting 
(x + 4.666666667) equal to 4.824704942 and -4.824704942.


Subproblem 1
x + 4.666666667 = 4.824704942

Simplifying
x + 4.666666667 = 4.824704942

Reorder the terms:
4.666666667 + x = 4.824704942

Solving
4.666666667 + x = 4.824704942

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 = 4.824704942 + -4.666666667

Combine like terms: 4.666666667 + -4.666666667 = 0.000000000
0.000000000 + x = 4.824704942 + -4.666666667
x = 4.824704942 + -4.666666667

Combine like terms: 4.824704942 + -4.666666667 = 0.158038275
x = 0.158038275

Simplifying
x = 0.158038275


Subproblem 2
x + 4.666666667 = -4.824704942

Simplifying
x + 4.666666667 = -4.824704942

Reorder the terms:
4.666666667 + x = -4.824704942

Solving
4.666666667 + x = -4.824704942

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 = -4.824704942 + -4.666666667

Combine like terms: 4.666666667 + -4.666666667 = 0.000000000
0.000000000 + x = -4.824704942 + -4.666666667
x = -4.824704942 + -4.666666667

Combine like terms: -4.824704942 + -4.666666667 = -9.491371609
x = -9.491371609

Simplifying
x = -9.491371609


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.158038275, -9.491371609}

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