6x^2-24x+23=0

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Solution for 6x^2-24x+23=0 equation: 


Simplifying
6x2 + -24x + 23 = 0

Reorder the terms:
23 + -24x + 6x2 = 0

Solving
23 + -24x + 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'.
3.833333333 + -4x + x2 = 0

Move the constant term to the right:

Add '-3.833333333' to each side of the equation.
3.833333333 + -4x + -3.833333333 + x2 = 0 + -3.833333333

Reorder the terms:
3.833333333 + -3.833333333 + -4x + x2 = 0 + -3.833333333

Combine like terms: 3.833333333 + -3.833333333 = 0.000000000
0.000000000 + -4x + x2 = 0 + -3.833333333
-4x + x2 = 0 + -3.833333333

Combine like terms: 0 + -3.833333333 = -3.833333333
-4x + x2 = -3.833333333

The x term is -4x.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4x + 4 + x2 = -3.833333333 + 4

Reorder the terms:
4 + -4x + x2 = -3.833333333 + 4

Combine like terms: -3.833333333 + 4 = 0.166666667
4 + -4x + x2 = 0.166666667

Factor a perfect square on the left side:
(x + -2)(x + -2) = 0.166666667

Calculate the square root of the right side: 0.408248291

Break this problem into two subproblems by setting 
(x + -2) equal to 0.408248291 and -0.408248291.


Subproblem 1
x + -2 = 0.408248291

Simplifying
x + -2 = 0.408248291

Reorder the terms:
-2 + x = 0.408248291

Solving
-2 + x = 0.408248291

Solving for variable 'x'.

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

Add '2' to each side of the equation.
-2 + 2 + x = 0.408248291 + 2

Combine like terms: -2 + 2 = 0
0 + x = 0.408248291 + 2
x = 0.408248291 + 2

Combine like terms: 0.408248291 + 2 = 2.408248291
x = 2.408248291

Simplifying
x = 2.408248291


Subproblem 2
x + -2 = -0.408248291

Simplifying
x + -2 = -0.408248291

Reorder the terms:
-2 + x = -0.408248291

Solving
-2 + x = -0.408248291

Solving for variable 'x'.

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

Add '2' to each side of the equation.
-2 + 2 + x = -0.408248291 + 2

Combine like terms: -2 + 2 = 0
0 + x = -0.408248291 + 2
x = -0.408248291 + 2

Combine like terms: -0.408248291 + 2 = 1.591751709
x = 1.591751709

Simplifying
x = 1.591751709


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.408248291, 1.591751709}

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