6x^2-29x+16=0

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Solution for 6x^2-29x+16=0 equation: 


Simplifying
6x2 + -29x + 16 = 0

Reorder the terms:
16 + -29x + 6x2 = 0

Solving
16 + -29x + 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'.
2.666666667 + -4.833333333x + x2 = 0

Move the constant term to the right:

Add '-2.666666667' to each side of the equation.
2.666666667 + -4.833333333x + -2.666666667 + x2 = 0 + -2.666666667

Reorder the terms:
2.666666667 + -2.666666667 + -4.833333333x + x2 = 0 + -2.666666667

Combine like terms: 2.666666667 + -2.666666667 = 0.000000000
0.000000000 + -4.833333333x + x2 = 0 + -2.666666667
-4.833333333x + x2 = 0 + -2.666666667

Combine like terms: 0 + -2.666666667 = -2.666666667
-4.833333333x + x2 = -2.666666667

The x term is -4.833333333x.  Take half its coefficient (-2.416666667).
Square it (5.840277779) and add it to both sides.

Add '5.840277779' to each side of the equation.
-4.833333333x + 5.840277779 + x2 = -2.666666667 + 5.840277779

Reorder the terms:
5.840277779 + -4.833333333x + x2 = -2.666666667 + 5.840277779

Combine like terms: -2.666666667 + 5.840277779 = 3.173611112
5.840277779 + -4.833333333x + x2 = 3.173611112

Factor a perfect square on the left side:
(x + -2.416666667)(x + -2.416666667) = 3.173611112

Calculate the square root of the right side: 1.781463194

Break this problem into two subproblems by setting 
(x + -2.416666667) equal to 1.781463194 and -1.781463194.


Subproblem 1
x + -2.416666667 = 1.781463194

Simplifying
x + -2.416666667 = 1.781463194

Reorder the terms:
-2.416666667 + x = 1.781463194

Solving
-2.416666667 + x = 1.781463194

Solving for variable 'x'.

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

Add '2.416666667' to each side of the equation.
-2.416666667 + 2.416666667 + x = 1.781463194 + 2.416666667

Combine like terms: -2.416666667 + 2.416666667 = 0.000000000
0.000000000 + x = 1.781463194 + 2.416666667
x = 1.781463194 + 2.416666667

Combine like terms: 1.781463194 + 2.416666667 = 4.198129861
x = 4.198129861

Simplifying
x = 4.198129861


Subproblem 2
x + -2.416666667 = -1.781463194

Simplifying
x + -2.416666667 = -1.781463194

Reorder the terms:
-2.416666667 + x = -1.781463194

Solving
-2.416666667 + x = -1.781463194

Solving for variable 'x'.

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

Add '2.416666667' to each side of the equation.
-2.416666667 + 2.416666667 + x = -1.781463194 + 2.416666667

Combine like terms: -2.416666667 + 2.416666667 = 0.000000000
0.000000000 + x = -1.781463194 + 2.416666667
x = -1.781463194 + 2.416666667

Combine like terms: -1.781463194 + 2.416666667 = 0.635203473
x = 0.635203473

Simplifying
x = 0.635203473


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.198129861, 0.635203473}

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