6X^2+2X-14=0

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


Simplifying
6X2 + 2X + -14 = 0

Reorder the terms:
-14 + 2X + 6X2 = 0

Solving
-14 + 2X + 6X2 = 0

Solving for variable 'X'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-7 + X + 3X2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-7 + X + 3X2)' equal to zero and attempt to solve:

Simplifying
-7 + X + 3X2 = 0

Solving
-7 + X + 3X2 = 0

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

Divide each side by '3'.
-2.333333333 + 0.3333333333X + X2 = 0

Move the constant term to the right:

Add '2.333333333' to each side of the equation.
-2.333333333 + 0.3333333333X + 2.333333333 + X2 = 0 + 2.333333333

Reorder the terms:
-2.333333333 + 2.333333333 + 0.3333333333X + X2 = 0 + 2.333333333

Combine like terms: -2.333333333 + 2.333333333 = 0.000000000
0.000000000 + 0.3333333333X + X2 = 0 + 2.333333333
0.3333333333X + X2 = 0 + 2.333333333

Combine like terms: 0 + 2.333333333 = 2.333333333
0.3333333333X + X2 = 2.333333333

The X term is X.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
0.3333333333X + 0.25 + X2 = 2.333333333 + 0.25

Reorder the terms:
0.25 + 0.3333333333X + X2 = 2.333333333 + 0.25

Combine like terms: 2.333333333 + 0.25 = 2.583333333
0.25 + 0.3333333333X + X2 = 2.583333333

Factor a perfect square on the left side:
(X + 0.5)(X + 0.5) = 2.583333333

Calculate the square root of the right side: 1.607275127

Break this problem into two subproblems by setting 
(X + 0.5) equal to 1.607275127 and -1.607275127.


Subproblem 1
X + 0.5 = 1.607275127

Simplifying
X + 0.5 = 1.607275127

Reorder the terms:
0.5 + X = 1.607275127

Solving
0.5 + X = 1.607275127

Solving for variable 'X'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + X = 1.607275127 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + X = 1.607275127 + -0.5
X = 1.607275127 + -0.5

Combine like terms: 1.607275127 + -0.5 = 1.107275127
X = 1.107275127

Simplifying
X = 1.107275127


Subproblem 2
X + 0.5 = -1.607275127

Simplifying
X + 0.5 = -1.607275127

Reorder the terms:
0.5 + X = -1.607275127

Solving
0.5 + X = -1.607275127

Solving for variable 'X'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + X = -1.607275127 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + X = -1.607275127 + -0.5
X = -1.607275127 + -0.5

Combine like terms: -1.607275127 + -0.5 = -2.107275127
X = -2.107275127

Simplifying
X = -2.107275127


Solution
The solution to the problem is based on the solutions
from the subproblems.
X = {1.107275127, -2.107275127}
Solution
X = {1.107275127, -2.107275127}

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