6x^2-26x+15=0

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Solution for 6x^2-26x+15=0 equation: 


Simplifying
6x2 + -26x + 15 = 0

Reorder the terms:
15 + -26x + 6x2 = 0

Solving
15 + -26x + 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'.
2.5 + -4.333333333x + x2 = 0

Move the constant term to the right:

Add '-2.5' to each side of the equation.
2.5 + -4.333333333x + -2.5 + x2 = 0 + -2.5

Reorder the terms:
2.5 + -2.5 + -4.333333333x + x2 = 0 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + -4.333333333x + x2 = 0 + -2.5
-4.333333333x + x2 = 0 + -2.5

Combine like terms: 0 + -2.5 = -2.5
-4.333333333x + x2 = -2.5

The x term is -4.333333333x.  Take half its coefficient (-2.166666667).
Square it (4.694444446) and add it to both sides.

Add '4.694444446' to each side of the equation.
-4.333333333x + 4.694444446 + x2 = -2.5 + 4.694444446

Reorder the terms:
4.694444446 + -4.333333333x + x2 = -2.5 + 4.694444446

Combine like terms: -2.5 + 4.694444446 = 2.194444446
4.694444446 + -4.333333333x + x2 = 2.194444446

Factor a perfect square on the left side:
(x + -2.166666667)(x + -2.166666667) = 2.194444446

Calculate the square root of the right side: 1.481365737

Break this problem into two subproblems by setting 
(x + -2.166666667) equal to 1.481365737 and -1.481365737.


Subproblem 1
x + -2.166666667 = 1.481365737

Simplifying
x + -2.166666667 = 1.481365737

Reorder the terms:
-2.166666667 + x = 1.481365737

Solving
-2.166666667 + x = 1.481365737

Solving for variable 'x'.

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

Add '2.166666667' to each side of the equation.
-2.166666667 + 2.166666667 + x = 1.481365737 + 2.166666667

Combine like terms: -2.166666667 + 2.166666667 = 0.000000000
0.000000000 + x = 1.481365737 + 2.166666667
x = 1.481365737 + 2.166666667

Combine like terms: 1.481365737 + 2.166666667 = 3.648032404
x = 3.648032404

Simplifying
x = 3.648032404


Subproblem 2
x + -2.166666667 = -1.481365737

Simplifying
x + -2.166666667 = -1.481365737

Reorder the terms:
-2.166666667 + x = -1.481365737

Solving
-2.166666667 + x = -1.481365737

Solving for variable 'x'.

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

Add '2.166666667' to each side of the equation.
-2.166666667 + 2.166666667 + x = -1.481365737 + 2.166666667

Combine like terms: -2.166666667 + 2.166666667 = 0.000000000
0.000000000 + x = -1.481365737 + 2.166666667
x = -1.481365737 + 2.166666667

Combine like terms: -1.481365737 + 2.166666667 = 0.68530093
x = 0.68530093

Simplifying
x = 0.68530093


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.648032404, 0.68530093}

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