3x^2-26x+12=0

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Solution for 3x^2-26x+12=0 equation: 


Simplifying
3x2 + -26x + 12 = 0

Reorder the terms:
12 + -26x + 3x2 = 0

Solving
12 + -26x + 3x2 = 0

Solving for variable 'x'.

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

Divide each side by '3'.
4 + -8.666666667x + x2 = 0

Move the constant term to the right:

Add '-4' to each side of the equation.
4 + -8.666666667x + -4 + x2 = 0 + -4

Reorder the terms:
4 + -4 + -8.666666667x + x2 = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -8.666666667x + x2 = 0 + -4
-8.666666667x + x2 = 0 + -4

Combine like terms: 0 + -4 = -4
-8.666666667x + x2 = -4

The x term is -8.666666667x.  Take half its coefficient (-4.333333334).
Square it (18.77777778) and add it to both sides.

Add '18.77777778' to each side of the equation.
-8.666666667x + 18.77777778 + x2 = -4 + 18.77777778

Reorder the terms:
18.77777778 + -8.666666667x + x2 = -4 + 18.77777778

Combine like terms: -4 + 18.77777778 = 14.77777778
18.77777778 + -8.666666667x + x2 = 14.77777778

Factor a perfect square on the left side:
(x + -4.333333334)(x + -4.333333334) = 14.77777778

Calculate the square root of the right side: 3.844187532

Break this problem into two subproblems by setting 
(x + -4.333333334) equal to 3.844187532 and -3.844187532.


Subproblem 1
x + -4.333333334 = 3.844187532

Simplifying
x + -4.333333334 = 3.844187532

Reorder the terms:
-4.333333334 + x = 3.844187532

Solving
-4.333333334 + x = 3.844187532

Solving for variable 'x'.

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

Add '4.333333334' to each side of the equation.
-4.333333334 + 4.333333334 + x = 3.844187532 + 4.333333334

Combine like terms: -4.333333334 + 4.333333334 = 0.000000000
0.000000000 + x = 3.844187532 + 4.333333334
x = 3.844187532 + 4.333333334

Combine like terms: 3.844187532 + 4.333333334 = 8.177520866
x = 8.177520866

Simplifying
x = 8.177520866


Subproblem 2
x + -4.333333334 = -3.844187532

Simplifying
x + -4.333333334 = -3.844187532

Reorder the terms:
-4.333333334 + x = -3.844187532

Solving
-4.333333334 + x = -3.844187532

Solving for variable 'x'.

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

Add '4.333333334' to each side of the equation.
-4.333333334 + 4.333333334 + x = -3.844187532 + 4.333333334

Combine like terms: -4.333333334 + 4.333333334 = 0.000000000
0.000000000 + x = -3.844187532 + 4.333333334
x = -3.844187532 + 4.333333334

Combine like terms: -3.844187532 + 4.333333334 = 0.489145802
x = 0.489145802

Simplifying
x = 0.489145802


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {8.177520866, 0.489145802}

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