6x^2-16x+5=0

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Solution for 6x^2-16x+5=0 equation: 


Simplifying
6x2 + -16x + 5 = 0

Reorder the terms:
5 + -16x + 6x2 = 0

Solving
5 + -16x + 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'.
0.8333333333 + -2.666666667x + x2 = 0

Move the constant term to the right:

Add '-0.8333333333' to each side of the equation.
0.8333333333 + -2.666666667x + -0.8333333333 + x2 = 0 + -0.8333333333

Reorder the terms:
0.8333333333 + -0.8333333333 + -2.666666667x + x2 = 0 + -0.8333333333

Combine like terms: 0.8333333333 + -0.8333333333 = 0.0000000000
0.0000000000 + -2.666666667x + x2 = 0 + -0.8333333333
-2.666666667x + x2 = 0 + -0.8333333333

Combine like terms: 0 + -0.8333333333 = -0.8333333333
-2.666666667x + x2 = -0.8333333333

The x term is -2.666666667x.  Take half its coefficient (-1.333333334).
Square it (1.777777780) and add it to both sides.

Add '1.777777780' to each side of the equation.
-2.666666667x + 1.777777780 + x2 = -0.8333333333 + 1.777777780

Reorder the terms:
1.777777780 + -2.666666667x + x2 = -0.8333333333 + 1.777777780

Combine like terms: -0.8333333333 + 1.777777780 = 0.9444444467
1.777777780 + -2.666666667x + x2 = 0.9444444467

Factor a perfect square on the left side:
(x + -1.333333334)(x + -1.333333334) = 0.9444444467

Calculate the square root of the right side: 0.971825317

Break this problem into two subproblems by setting 
(x + -1.333333334) equal to 0.971825317 and -0.971825317.


Subproblem 1
x + -1.333333334 = 0.971825317

Simplifying
x + -1.333333334 = 0.971825317

Reorder the terms:
-1.333333334 + x = 0.971825317

Solving
-1.333333334 + x = 0.971825317

Solving for variable 'x'.

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

Add '1.333333334' to each side of the equation.
-1.333333334 + 1.333333334 + x = 0.971825317 + 1.333333334

Combine like terms: -1.333333334 + 1.333333334 = 0.000000000
0.000000000 + x = 0.971825317 + 1.333333334
x = 0.971825317 + 1.333333334

Combine like terms: 0.971825317 + 1.333333334 = 2.305158651
x = 2.305158651

Simplifying
x = 2.305158651


Subproblem 2
x + -1.333333334 = -0.971825317

Simplifying
x + -1.333333334 = -0.971825317

Reorder the terms:
-1.333333334 + x = -0.971825317

Solving
-1.333333334 + x = -0.971825317

Solving for variable 'x'.

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

Add '1.333333334' to each side of the equation.
-1.333333334 + 1.333333334 + x = -0.971825317 + 1.333333334

Combine like terms: -1.333333334 + 1.333333334 = 0.000000000
0.000000000 + x = -0.971825317 + 1.333333334
x = -0.971825317 + 1.333333334

Combine like terms: -0.971825317 + 1.333333334 = 0.361508017
x = 0.361508017

Simplifying
x = 0.361508017


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.305158651, 0.361508017}

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