2X^2+6X-128=0

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Solution for 2X^2+6X-128=0 equation: 


Simplifying
2X2 + 6X + -128 = 0

Reorder the terms:
-128 + 6X + 2X2 = 0

Solving
-128 + 6X + 2X2 = 0

Solving for variable 'X'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-64 + 3X + X2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-64 + 3X + X2)' equal to zero and attempt to solve:

Simplifying
-64 + 3X + X2 = 0

Solving
-64 + 3X + X2 = 0

Begin completing the square.

Move the constant term to the right:

Add '64' to each side of the equation.
-64 + 3X + 64 + X2 = 0 + 64

Reorder the terms:
-64 + 64 + 3X + X2 = 0 + 64

Combine like terms: -64 + 64 = 0
0 + 3X + X2 = 0 + 64
3X + X2 = 0 + 64

Combine like terms: 0 + 64 = 64
3X + X2 = 64

The X term is 3X.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3X + 2.25 + X2 = 64 + 2.25

Reorder the terms:
2.25 + 3X + X2 = 64 + 2.25

Combine like terms: 64 + 2.25 = 66.25
2.25 + 3X + X2 = 66.25

Factor a perfect square on the left side:
(X + 1.5)(X + 1.5) = 66.25

Calculate the square root of the right side: 8.139410298

Break this problem into two subproblems by setting 
(X + 1.5) equal to 8.139410298 and -8.139410298.


Subproblem 1
X + 1.5 = 8.139410298

Simplifying
X + 1.5 = 8.139410298

Reorder the terms:
1.5 + X = 8.139410298

Solving
1.5 + X = 8.139410298

Solving for variable 'X'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + X = 8.139410298 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + X = 8.139410298 + -1.5
X = 8.139410298 + -1.5

Combine like terms: 8.139410298 + -1.5 = 6.639410298
X = 6.639410298

Simplifying
X = 6.639410298


Subproblem 2
X + 1.5 = -8.139410298

Simplifying
X + 1.5 = -8.139410298

Reorder the terms:
1.5 + X = -8.139410298

Solving
1.5 + X = -8.139410298

Solving for variable 'X'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + X = -8.139410298 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + X = -8.139410298 + -1.5
X = -8.139410298 + -1.5

Combine like terms: -8.139410298 + -1.5 = -9.639410298
X = -9.639410298

Simplifying
X = -9.639410298


Solution
The solution to the problem is based on the solutions
from the subproblems.
X = {6.639410298, -9.639410298}
Solution
X = {6.639410298, -9.639410298}

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