3x^2-14x+6=0

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Solution for 3x^2-14x+6=0 equation: 


Simplifying
3x2 + -14x + 6 = 0

Reorder the terms:
6 + -14x + 3x2 = 0

Solving
6 + -14x + 3x2 = 0

Solving for variable 'x'.

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

Divide each side by '3'.
2 + -4.666666667x + x2 = 0

Move the constant term to the right:

Add '-2' to each side of the equation.
2 + -4.666666667x + -2 + x2 = 0 + -2

Reorder the terms:
2 + -2 + -4.666666667x + x2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -4.666666667x + x2 = 0 + -2
-4.666666667x + x2 = 0 + -2

Combine like terms: 0 + -2 = -2
-4.666666667x + x2 = -2

The x term is -4.666666667x.  Take half its coefficient (-2.333333334).
Square it (5.444444448) and add it to both sides.

Add '5.444444448' to each side of the equation.
-4.666666667x + 5.444444448 + x2 = -2 + 5.444444448

Reorder the terms:
5.444444448 + -4.666666667x + x2 = -2 + 5.444444448

Combine like terms: -2 + 5.444444448 = 3.444444448
5.444444448 + -4.666666667x + x2 = 3.444444448

Factor a perfect square on the left side:
(x + -2.333333334)(x + -2.333333334) = 3.444444448

Calculate the square root of the right side: 1.855921455

Break this problem into two subproblems by setting 
(x + -2.333333334) equal to 1.855921455 and -1.855921455.


Subproblem 1
x + -2.333333334 = 1.855921455

Simplifying
x + -2.333333334 = 1.855921455

Reorder the terms:
-2.333333334 + x = 1.855921455

Solving
-2.333333334 + x = 1.855921455

Solving for variable 'x'.

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

Add '2.333333334' to each side of the equation.
-2.333333334 + 2.333333334 + x = 1.855921455 + 2.333333334

Combine like terms: -2.333333334 + 2.333333334 = 0.000000000
0.000000000 + x = 1.855921455 + 2.333333334
x = 1.855921455 + 2.333333334

Combine like terms: 1.855921455 + 2.333333334 = 4.189254789
x = 4.189254789

Simplifying
x = 4.189254789


Subproblem 2
x + -2.333333334 = -1.855921455

Simplifying
x + -2.333333334 = -1.855921455

Reorder the terms:
-2.333333334 + x = -1.855921455

Solving
-2.333333334 + x = -1.855921455

Solving for variable 'x'.

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

Add '2.333333334' to each side of the equation.
-2.333333334 + 2.333333334 + x = -1.855921455 + 2.333333334

Combine like terms: -2.333333334 + 2.333333334 = 0.000000000
0.000000000 + x = -1.855921455 + 2.333333334
x = -1.855921455 + 2.333333334

Combine like terms: -1.855921455 + 2.333333334 = 0.477411879
x = 0.477411879

Simplifying
x = 0.477411879


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.189254789, 0.477411879}

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