6X^2+30X-44=0

Solution for 6X^2+30X-44=0 equation:

Simplifying
6X2 + 30X + -44 = 0

Reorder the terms:
-44 + 30X + 6X2 = 0

Solving
-44 + 30X + 6X2 = 0

Solving for variable 'X'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-22 + 15X + 3X2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-22 + 15X + 3X2)' equal to zero and attempt to solve:

Simplifying
-22 + 15X + 3X2 = 0

Solving
-22 + 15X + 3X2 = 0

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

Divide each side by '3'.
-7.333333333 + 5X + X2 = 0

Move the constant term to the right:

Add '7.333333333' to each side of the equation.
-7.333333333 + 5X + 7.333333333 + X2 = 0 + 7.333333333

Reorder the terms:
-7.333333333 + 7.333333333 + 5X + X2 = 0 + 7.333333333

Combine like terms: -7.333333333 + 7.333333333 = 0.000000000
0.000000000 + 5X + X2 = 0 + 7.333333333
5X + X2 = 0 + 7.333333333

Combine like terms: 0 + 7.333333333 = 7.333333333
5X + X2 = 7.333333333

The X term is 5X.  Take half its coefficient (2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
5X + 6.25 + X2 = 7.333333333 + 6.25

Reorder the terms:
6.25 + 5X + X2 = 7.333333333 + 6.25

Combine like terms: 7.333333333 + 6.25 = 13.583333333
6.25 + 5X + X2 = 13.583333333

Factor a perfect square on the left side:
(X + 2.5)(X + 2.5) = 13.583333333

Calculate the square root of the right side: 3.685557398

Break this problem into two subproblems by setting 
(X + 2.5) equal to 3.685557398 and -3.685557398.

Subproblem 1
X + 2.5 = 3.685557398

Simplifying
X + 2.5 = 3.685557398

Reorder the terms:
2.5 + X = 3.685557398

Solving
2.5 + X = 3.685557398

Solving for variable 'X'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + X = 3.685557398 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + X = 3.685557398 + -2.5
X = 3.685557398 + -2.5

Combine like terms: 3.685557398 + -2.5 = 1.185557398
X = 1.185557398

Simplifying
X = 1.185557398

Subproblem 2
X + 2.5 = -3.685557398

Simplifying
X + 2.5 = -3.685557398

Reorder the terms:
2.5 + X = -3.685557398

Solving
2.5 + X = -3.685557398

Solving for variable 'X'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + X = -3.685557398 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + X = -3.685557398 + -2.5
X = -3.685557398 + -2.5

Combine like terms: -3.685557398 + -2.5 = -6.185557398
X = -6.185557398

Simplifying
X = -6.185557398

Solution
The solution to the problem is based on the solutions
from the subproblems.
X = {1.185557398, -6.185557398}
Solution
X = {1.185557398, -6.185557398}