6X^2+16X-4=0

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Solution for 6X^2+16X-4=0 equation: 


Simplifying
6X2 + 16X + -4 = 0

Reorder the terms:
-4 + 16X + 6X2 = 0

Solving
-4 + 16X + 6X2 = 0

Solving for variable 'X'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-2 + 8X + 3X2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-2 + 8X + 3X2)' equal to zero and attempt to solve:

Simplifying
-2 + 8X + 3X2 = 0

Solving
-2 + 8X + 3X2 = 0

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

Divide each side by '3'.
-0.6666666667 + 2.666666667X + X2 = 0

Move the constant term to the right:

Add '0.6666666667' to each side of the equation.
-0.6666666667 + 2.666666667X + 0.6666666667 + X2 = 0 + 0.6666666667

Reorder the terms:
-0.6666666667 + 0.6666666667 + 2.666666667X + X2 = 0 + 0.6666666667

Combine like terms: -0.6666666667 + 0.6666666667 = 0.0000000000
0.0000000000 + 2.666666667X + X2 = 0 + 0.6666666667
2.666666667X + X2 = 0 + 0.6666666667

Combine like terms: 0 + 0.6666666667 = 0.6666666667
2.666666667X + X2 = 0.6666666667

The X term is 2.666666667X.  Take half its coefficient (1.333333334).
Square it (1.777777780) and add it to both sides.

Add '1.777777780' to each side of the equation.
2.666666667X + 1.777777780 + X2 = 0.6666666667 + 1.777777780

Reorder the terms:
1.777777780 + 2.666666667X + X2 = 0.6666666667 + 1.777777780

Combine like terms: 0.6666666667 + 1.777777780 = 2.4444444467
1.777777780 + 2.666666667X + X2 = 2.4444444467

Factor a perfect square on the left side:
(X + 1.333333334)(X + 1.333333334) = 2.4444444467

Calculate the square root of the right side: 1.563471921

Break this problem into two subproblems by setting 
(X + 1.333333334) equal to 1.563471921 and -1.563471921.


Subproblem 1
X + 1.333333334 = 1.563471921

Simplifying
X + 1.333333334 = 1.563471921

Reorder the terms:
1.333333334 + X = 1.563471921

Solving
1.333333334 + X = 1.563471921

Solving for variable 'X'.

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

Add '-1.333333334' to each side of the equation.
1.333333334 + -1.333333334 + X = 1.563471921 + -1.333333334

Combine like terms: 1.333333334 + -1.333333334 = 0.000000000
0.000000000 + X = 1.563471921 + -1.333333334
X = 1.563471921 + -1.333333334

Combine like terms: 1.563471921 + -1.333333334 = 0.230138587
X = 0.230138587

Simplifying
X = 0.230138587


Subproblem 2
X + 1.333333334 = -1.563471921

Simplifying
X + 1.333333334 = -1.563471921

Reorder the terms:
1.333333334 + X = -1.563471921

Solving
1.333333334 + X = -1.563471921

Solving for variable 'X'.

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

Add '-1.333333334' to each side of the equation.
1.333333334 + -1.333333334 + X = -1.563471921 + -1.333333334

Combine like terms: 1.333333334 + -1.333333334 = 0.000000000
0.000000000 + X = -1.563471921 + -1.333333334
X = -1.563471921 + -1.333333334

Combine like terms: -1.563471921 + -1.333333334 = -2.896805255
X = -2.896805255

Simplifying
X = -2.896805255


Solution
The solution to the problem is based on the solutions
from the subproblems.
X = {0.230138587, -2.896805255}
Solution
X = {0.230138587, -2.896805255}

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