6x^2-34x+10=0

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Solution for 6x^2-34x+10=0 equation: 


Simplifying
6x2 + -34x + 10 = 0

Reorder the terms:
10 + -34x + 6x2 = 0

Solving
10 + -34x + 6x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(5 + -17x + 3x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(5 + -17x + 3x2)' equal to zero and attempt to solve:

Simplifying
5 + -17x + 3x2 = 0

Solving
5 + -17x + 3x2 = 0

Begin completing the square.  Divide all terms by
3 the coefficient of the squared term: 

Divide each side by '3'.
1.666666667 + -5.666666667x + x2 = 0

Move the constant term to the right:

Add '-1.666666667' to each side of the equation.
1.666666667 + -5.666666667x + -1.666666667 + x2 = 0 + -1.666666667

Reorder the terms:
1.666666667 + -1.666666667 + -5.666666667x + x2 = 0 + -1.666666667

Combine like terms: 1.666666667 + -1.666666667 = 0.000000000
0.000000000 + -5.666666667x + x2 = 0 + -1.666666667
-5.666666667x + x2 = 0 + -1.666666667

Combine like terms: 0 + -1.666666667 = -1.666666667
-5.666666667x + x2 = -1.666666667

The x term is -5.666666667x.  Take half its coefficient (-2.833333334).
Square it (8.027777782) and add it to both sides.

Add '8.027777782' to each side of the equation.
-5.666666667x + 8.027777782 + x2 = -1.666666667 + 8.027777782

Reorder the terms:
8.027777782 + -5.666666667x + x2 = -1.666666667 + 8.027777782

Combine like terms: -1.666666667 + 8.027777782 = 6.361111115
8.027777782 + -5.666666667x + x2 = 6.361111115

Factor a perfect square on the left side:
(x + -2.833333334)(x + -2.833333334) = 6.361111115

Calculate the square root of the right side: 2.522124326

Break this problem into two subproblems by setting 
(x + -2.833333334) equal to 2.522124326 and -2.522124326.


Subproblem 1
x + -2.833333334 = 2.522124326

Simplifying
x + -2.833333334 = 2.522124326

Reorder the terms:
-2.833333334 + x = 2.522124326

Solving
-2.833333334 + x = 2.522124326

Solving for variable 'x'.

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

Add '2.833333334' to each side of the equation.
-2.833333334 + 2.833333334 + x = 2.522124326 + 2.833333334

Combine like terms: -2.833333334 + 2.833333334 = 0.000000000
0.000000000 + x = 2.522124326 + 2.833333334
x = 2.522124326 + 2.833333334

Combine like terms: 2.522124326 + 2.833333334 = 5.35545766
x = 5.35545766

Simplifying
x = 5.35545766


Subproblem 2
x + -2.833333334 = -2.522124326

Simplifying
x + -2.833333334 = -2.522124326

Reorder the terms:
-2.833333334 + x = -2.522124326

Solving
-2.833333334 + x = -2.522124326

Solving for variable 'x'.

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

Add '2.833333334' to each side of the equation.
-2.833333334 + 2.833333334 + x = -2.522124326 + 2.833333334

Combine like terms: -2.833333334 + 2.833333334 = 0.000000000
0.000000000 + x = -2.522124326 + 2.833333334
x = -2.522124326 + 2.833333334

Combine like terms: -2.522124326 + 2.833333334 = 0.311209008
x = 0.311209008

Simplifying
x = 0.311209008


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.35545766, 0.311209008}
Solution
x = {5.35545766, 0.311209008}

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