6x^2-40x+11=0

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Solution for 6x^2-40x+11=0 equation: 


Simplifying
6x2 + -40x + 11 = 0

Reorder the terms:
11 + -40x + 6x2 = 0

Solving
11 + -40x + 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'.
1.833333333 + -6.666666667x + x2 = 0

Move the constant term to the right:

Add '-1.833333333' to each side of the equation.
1.833333333 + -6.666666667x + -1.833333333 + x2 = 0 + -1.833333333

Reorder the terms:
1.833333333 + -1.833333333 + -6.666666667x + x2 = 0 + -1.833333333

Combine like terms: 1.833333333 + -1.833333333 = 0.000000000
0.000000000 + -6.666666667x + x2 = 0 + -1.833333333
-6.666666667x + x2 = 0 + -1.833333333

Combine like terms: 0 + -1.833333333 = -1.833333333
-6.666666667x + x2 = -1.833333333

The x term is -6.666666667x.  Take half its coefficient (-3.333333334).
Square it (11.11111112) and add it to both sides.

Add '11.11111112' to each side of the equation.
-6.666666667x + 11.11111112 + x2 = -1.833333333 + 11.11111112

Reorder the terms:
11.11111112 + -6.666666667x + x2 = -1.833333333 + 11.11111112

Combine like terms: -1.833333333 + 11.11111112 = 9.277777787
11.11111112 + -6.666666667x + x2 = 9.277777787

Factor a perfect square on the left side:
(x + -3.333333334)(x + -3.333333334) = 9.277777787

Calculate the square root of the right side: 3.045944482

Break this problem into two subproblems by setting 
(x + -3.333333334) equal to 3.045944482 and -3.045944482.


Subproblem 1
x + -3.333333334 = 3.045944482

Simplifying
x + -3.333333334 = 3.045944482

Reorder the terms:
-3.333333334 + x = 3.045944482

Solving
-3.333333334 + x = 3.045944482

Solving for variable 'x'.

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

Add '3.333333334' to each side of the equation.
-3.333333334 + 3.333333334 + x = 3.045944482 + 3.333333334

Combine like terms: -3.333333334 + 3.333333334 = 0.000000000
0.000000000 + x = 3.045944482 + 3.333333334
x = 3.045944482 + 3.333333334

Combine like terms: 3.045944482 + 3.333333334 = 6.379277816
x = 6.379277816

Simplifying
x = 6.379277816


Subproblem 2
x + -3.333333334 = -3.045944482

Simplifying
x + -3.333333334 = -3.045944482

Reorder the terms:
-3.333333334 + x = -3.045944482

Solving
-3.333333334 + x = -3.045944482

Solving for variable 'x'.

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

Add '3.333333334' to each side of the equation.
-3.333333334 + 3.333333334 + x = -3.045944482 + 3.333333334

Combine like terms: -3.333333334 + 3.333333334 = 0.000000000
0.000000000 + x = -3.045944482 + 3.333333334
x = -3.045944482 + 3.333333334

Combine like terms: -3.045944482 + 3.333333334 = 0.287388852
x = 0.287388852

Simplifying
x = 0.287388852


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.379277816, 0.287388852}

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