6x^2-14x-2=0

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


Simplifying
6x2 + -14x + -2 = 0

Reorder the terms:
-2 + -14x + 6x2 = 0

Solving
-2 + -14x + 6x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-1 + -7x + 3x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-1 + -7x + 3x2)' equal to zero and attempt to solve:

Simplifying
-1 + -7x + 3x2 = 0

Solving
-1 + -7x + 3x2 = 0

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

Divide each side by '3'.
-0.3333333333 + -2.333333333x + x2 = 0

Move the constant term to the right:

Add '0.3333333333' to each side of the equation.
-0.3333333333 + -2.333333333x + 0.3333333333 + x2 = 0 + 0.3333333333

Reorder the terms:
-0.3333333333 + 0.3333333333 + -2.333333333x + x2 = 0 + 0.3333333333

Combine like terms: -0.3333333333 + 0.3333333333 = 0.0000000000
0.0000000000 + -2.333333333x + x2 = 0 + 0.3333333333
-2.333333333x + x2 = 0 + 0.3333333333

Combine like terms: 0 + 0.3333333333 = 0.3333333333
-2.333333333x + x2 = 0.3333333333

The x term is -2.333333333x.  Take half its coefficient (-1.166666667).
Square it (1.361111112) and add it to both sides.

Add '1.361111112' to each side of the equation.
-2.333333333x + 1.361111112 + x2 = 0.3333333333 + 1.361111112

Reorder the terms:
1.361111112 + -2.333333333x + x2 = 0.3333333333 + 1.361111112

Combine like terms: 0.3333333333 + 1.361111112 = 1.6944444453
1.361111112 + -2.333333333x + x2 = 1.6944444453

Factor a perfect square on the left side:
(x + -1.166666667)(x + -1.166666667) = 1.6944444453

Calculate the square root of the right side: 1.30170828

Break this problem into two subproblems by setting 
(x + -1.166666667) equal to 1.30170828 and -1.30170828.


Subproblem 1
x + -1.166666667 = 1.30170828

Simplifying
x + -1.166666667 = 1.30170828

Reorder the terms:
-1.166666667 + x = 1.30170828

Solving
-1.166666667 + x = 1.30170828

Solving for variable 'x'.

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

Add '1.166666667' to each side of the equation.
-1.166666667 + 1.166666667 + x = 1.30170828 + 1.166666667

Combine like terms: -1.166666667 + 1.166666667 = 0.000000000
0.000000000 + x = 1.30170828 + 1.166666667
x = 1.30170828 + 1.166666667

Combine like terms: 1.30170828 + 1.166666667 = 2.468374947
x = 2.468374947

Simplifying
x = 2.468374947


Subproblem 2
x + -1.166666667 = -1.30170828

Simplifying
x + -1.166666667 = -1.30170828

Reorder the terms:
-1.166666667 + x = -1.30170828

Solving
-1.166666667 + x = -1.30170828

Solving for variable 'x'.

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

Add '1.166666667' to each side of the equation.
-1.166666667 + 1.166666667 + x = -1.30170828 + 1.166666667

Combine like terms: -1.166666667 + 1.166666667 = 0.000000000
0.000000000 + x = -1.30170828 + 1.166666667
x = -1.30170828 + 1.166666667

Combine like terms: -1.30170828 + 1.166666667 = -0.135041613
x = -0.135041613

Simplifying
x = -0.135041613


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.468374947, -0.135041613}
Solution
x = {2.468374947, -0.135041613}

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