3x^2-26x+22=0

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Solution for 3x^2-26x+22=0 equation: 


Simplifying
3x2 + -26x + 22 = 0

Reorder the terms:
22 + -26x + 3x2 = 0

Solving
22 + -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'.
7.333333333 + -8.666666667x + x2 = 0

Move the constant term to the right:

Add '-7.333333333' to each side of the equation.
7.333333333 + -8.666666667x + -7.333333333 + x2 = 0 + -7.333333333

Reorder the terms:
7.333333333 + -7.333333333 + -8.666666667x + x2 = 0 + -7.333333333

Combine like terms: 7.333333333 + -7.333333333 = 0.000000000
0.000000000 + -8.666666667x + x2 = 0 + -7.333333333
-8.666666667x + x2 = 0 + -7.333333333

Combine like terms: 0 + -7.333333333 = -7.333333333
-8.666666667x + x2 = -7.333333333

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 = -7.333333333 + 18.77777778

Reorder the terms:
18.77777778 + -8.666666667x + x2 = -7.333333333 + 18.77777778

Combine like terms: -7.333333333 + 18.77777778 = 11.444444447
18.77777778 + -8.666666667x + x2 = 11.444444447

Factor a perfect square on the left side:
(x + -4.333333334)(x + -4.333333334) = 11.444444447

Calculate the square root of the right side: 3.382963855

Break this problem into two subproblems by setting 
(x + -4.333333334) equal to 3.382963855 and -3.382963855.


Subproblem 1
x + -4.333333334 = 3.382963855

Simplifying
x + -4.333333334 = 3.382963855

Reorder the terms:
-4.333333334 + x = 3.382963855

Solving
-4.333333334 + x = 3.382963855

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 = 3.382963855 + 4.333333334

Combine like terms: -4.333333334 + 4.333333334 = 0.000000000
0.000000000 + x = 3.382963855 + 4.333333334
x = 3.382963855 + 4.333333334

Combine like terms: 3.382963855 + 4.333333334 = 7.716297189
x = 7.716297189

Simplifying
x = 7.716297189


Subproblem 2
x + -4.333333334 = -3.382963855

Simplifying
x + -4.333333334 = -3.382963855

Reorder the terms:
-4.333333334 + x = -3.382963855

Solving
-4.333333334 + x = -3.382963855

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 = -3.382963855 + 4.333333334

Combine like terms: -4.333333334 + 4.333333334 = 0.000000000
0.000000000 + x = -3.382963855 + 4.333333334
x = -3.382963855 + 4.333333334

Combine like terms: -3.382963855 + 4.333333334 = 0.950369479
x = 0.950369479

Simplifying
x = 0.950369479


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {7.716297189, 0.950369479}

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