2X^2+12X+14=0

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Solution for 2X^2+12X+14=0 equation: 


Simplifying
2X2 + 12X + 14 = 0

Reorder the terms:
14 + 12X + 2X2 = 0

Solving
14 + 12X + 2X2 = 0

Solving for variable 'X'.

Factor out the Greatest Common Factor (GCF), '2'.
2(7 + 6X + X2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(7 + 6X + X2)' equal to zero and attempt to solve:

Simplifying
7 + 6X + X2 = 0

Solving
7 + 6X + X2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-7' to each side of the equation.
7 + 6X + -7 + X2 = 0 + -7

Reorder the terms:
7 + -7 + 6X + X2 = 0 + -7

Combine like terms: 7 + -7 = 0
0 + 6X + X2 = 0 + -7
6X + X2 = 0 + -7

Combine like terms: 0 + -7 = -7
6X + X2 = -7

The X term is 6X.  Take half its coefficient (3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
6X + 9 + X2 = -7 + 9

Reorder the terms:
9 + 6X + X2 = -7 + 9

Combine like terms: -7 + 9 = 2
9 + 6X + X2 = 2

Factor a perfect square on the left side:
(X + 3)(X + 3) = 2

Calculate the square root of the right side: 1.414213562

Break this problem into two subproblems by setting 
(X + 3) equal to 1.414213562 and -1.414213562.


Subproblem 1
X + 3 = 1.414213562

Simplifying
X + 3 = 1.414213562

Reorder the terms:
3 + X = 1.414213562

Solving
3 + X = 1.414213562

Solving for variable 'X'.

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

Add '-3' to each side of the equation.
3 + -3 + X = 1.414213562 + -3

Combine like terms: 3 + -3 = 0
0 + X = 1.414213562 + -3
X = 1.414213562 + -3

Combine like terms: 1.414213562 + -3 = -1.585786438
X = -1.585786438

Simplifying
X = -1.585786438


Subproblem 2
X + 3 = -1.414213562

Simplifying
X + 3 = -1.414213562

Reorder the terms:
3 + X = -1.414213562

Solving
3 + X = -1.414213562

Solving for variable 'X'.

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

Add '-3' to each side of the equation.
3 + -3 + X = -1.414213562 + -3

Combine like terms: 3 + -3 = 0
0 + X = -1.414213562 + -3
X = -1.414213562 + -3

Combine like terms: -1.414213562 + -3 = -4.414213562
X = -4.414213562

Simplifying
X = -4.414213562


Solution
The solution to the problem is based on the solutions
from the subproblems.
X = {-1.585786438, -4.414213562}
Solution
X = {-1.585786438, -4.414213562}

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