12x^2-256x+350=0

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Solution for 12x^2-256x+350=0 equation: 


Simplifying
12x2 + -256x + 350 = 0

Reorder the terms:
350 + -256x + 12x2 = 0

Solving
350 + -256x + 12x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(175 + -128x + 6x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(175 + -128x + 6x2)' equal to zero and attempt to solve:

Simplifying
175 + -128x + 6x2 = 0

Solving
175 + -128x + 6x2 = 0

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

Divide each side by '6'.
29.16666667 + -21.33333333x + x2 = 0

Move the constant term to the right:

Add '-29.16666667' to each side of the equation.
29.16666667 + -21.33333333x + -29.16666667 + x2 = 0 + -29.16666667

Reorder the terms:
29.16666667 + -29.16666667 + -21.33333333x + x2 = 0 + -29.16666667

Combine like terms: 29.16666667 + -29.16666667 = 0.00000000
0.00000000 + -21.33333333x + x2 = 0 + -29.16666667
-21.33333333x + x2 = 0 + -29.16666667

Combine like terms: 0 + -29.16666667 = -29.16666667
-21.33333333x + x2 = -29.16666667

The x term is -21.33333333x.  Take half its coefficient (-10.66666667).
Square it (113.7777778) and add it to both sides.

Add '113.7777778' to each side of the equation.
-21.33333333x + 113.7777778 + x2 = -29.16666667 + 113.7777778

Reorder the terms:
113.7777778 + -21.33333333x + x2 = -29.16666667 + 113.7777778

Combine like terms: -29.16666667 + 113.7777778 = 84.61111113
113.7777778 + -21.33333333x + x2 = 84.61111113

Factor a perfect square on the left side:
(x + -10.66666667)(x + -10.66666667) = 84.61111113

Calculate the square root of the right side: 9.198429819

Break this problem into two subproblems by setting 
(x + -10.66666667) equal to 9.198429819 and -9.198429819.


Subproblem 1
x + -10.66666667 = 9.198429819

Simplifying
x + -10.66666667 = 9.198429819

Reorder the terms:
-10.66666667 + x = 9.198429819

Solving
-10.66666667 + x = 9.198429819

Solving for variable 'x'.

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

Add '10.66666667' to each side of the equation.
-10.66666667 + 10.66666667 + x = 9.198429819 + 10.66666667

Combine like terms: -10.66666667 + 10.66666667 = 0.00000000
0.00000000 + x = 9.198429819 + 10.66666667
x = 9.198429819 + 10.66666667

Combine like terms: 9.198429819 + 10.66666667 = 19.865096489
x = 19.865096489

Simplifying
x = 19.865096489


Subproblem 2
x + -10.66666667 = -9.198429819

Simplifying
x + -10.66666667 = -9.198429819

Reorder the terms:
-10.66666667 + x = -9.198429819

Solving
-10.66666667 + x = -9.198429819

Solving for variable 'x'.

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

Add '10.66666667' to each side of the equation.
-10.66666667 + 10.66666667 + x = -9.198429819 + 10.66666667

Combine like terms: -10.66666667 + 10.66666667 = 0.00000000
0.00000000 + x = -9.198429819 + 10.66666667
x = -9.198429819 + 10.66666667

Combine like terms: -9.198429819 + 10.66666667 = 1.468236851
x = 1.468236851

Simplifying
x = 1.468236851


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {19.865096489, 1.468236851}
Solution
x = {19.865096489, 1.468236851}

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