0=6x^2+12x-14

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Solution for 0=6x^2+12x-14 equation: 


Simplifying
0 = 6x2 + 12x + -14

Reorder the terms:
0 = -14 + 12x + 6x2

Solving
0 = -14 + 12x + 6x2

Solving for variable 'x'.

Combine like terms: 0 + 14 = 14
14 + -12x + -6x2 = -14 + 12x + 6x2 + 14 + -12x + -6x2

Reorder the terms:
14 + -12x + -6x2 = -14 + 14 + 12x + -12x + 6x2 + -6x2

Combine like terms: -14 + 14 = 0
14 + -12x + -6x2 = 0 + 12x + -12x + 6x2 + -6x2
14 + -12x + -6x2 = 12x + -12x + 6x2 + -6x2

Combine like terms: 12x + -12x = 0
14 + -12x + -6x2 = 0 + 6x2 + -6x2
14 + -12x + -6x2 = 6x2 + -6x2

Combine like terms: 6x2 + -6x2 = 0
14 + -12x + -6x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(7 + -6x + -3x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(7 + -6x + -3x2)' equal to zero and attempt to solve:

Simplifying
7 + -6x + -3x2 = 0

Solving
7 + -6x + -3x2 = 0

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

Divide each side by '-3'.
-2.333333333 + 2x + x2 = 0

Move the constant term to the right:

Add '2.333333333' to each side of the equation.
-2.333333333 + 2x + 2.333333333 + x2 = 0 + 2.333333333

Reorder the terms:
-2.333333333 + 2.333333333 + 2x + x2 = 0 + 2.333333333

Combine like terms: -2.333333333 + 2.333333333 = 0.000000000
0.000000000 + 2x + x2 = 0 + 2.333333333
2x + x2 = 0 + 2.333333333

Combine like terms: 0 + 2.333333333 = 2.333333333
2x + x2 = 2.333333333

The x term is 2x.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2x + 1 + x2 = 2.333333333 + 1

Reorder the terms:
1 + 2x + x2 = 2.333333333 + 1

Combine like terms: 2.333333333 + 1 = 3.333333333
1 + 2x + x2 = 3.333333333

Factor a perfect square on the left side:
(x + 1)(x + 1) = 3.333333333

Calculate the square root of the right side: 1.825741858

Break this problem into two subproblems by setting 
(x + 1) equal to 1.825741858 and -1.825741858.


Subproblem 1
x + 1 = 1.825741858

Simplifying
x + 1 = 1.825741858

Reorder the terms:
1 + x = 1.825741858

Solving
1 + x = 1.825741858

Solving for variable 'x'.

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

Add '-1' to each side of the equation.
1 + -1 + x = 1.825741858 + -1

Combine like terms: 1 + -1 = 0
0 + x = 1.825741858 + -1
x = 1.825741858 + -1

Combine like terms: 1.825741858 + -1 = 0.825741858
x = 0.825741858

Simplifying
x = 0.825741858


Subproblem 2
x + 1 = -1.825741858

Simplifying
x + 1 = -1.825741858

Reorder the terms:
1 + x = -1.825741858

Solving
1 + x = -1.825741858

Solving for variable 'x'.

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

Add '-1' to each side of the equation.
1 + -1 + x = -1.825741858 + -1

Combine like terms: 1 + -1 = 0
0 + x = -1.825741858 + -1
x = -1.825741858 + -1

Combine like terms: -1.825741858 + -1 = -2.825741858
x = -2.825741858

Simplifying
x = -2.825741858


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.825741858, -2.825741858}
Solution
x = {0.825741858, -2.825741858}

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