4x^2+30x-44=0

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Solution for 4x^2+30x-44=0 equation: 


Simplifying
4x2 + 30x + -44 = 0

Reorder the terms:
-44 + 30x + 4x2 = 0

Solving
-44 + 30x + 4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-22 + 15x + 2x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-22 + 15x + 2x2)' equal to zero and attempt to solve:

Simplifying
-22 + 15x + 2x2 = 0

Solving
-22 + 15x + 2x2 = 0

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

Divide each side by '2'.
-11 + 7.5x + x2 = 0

Move the constant term to the right:

Add '11' to each side of the equation.
-11 + 7.5x + 11 + x2 = 0 + 11

Reorder the terms:
-11 + 11 + 7.5x + x2 = 0 + 11

Combine like terms: -11 + 11 = 0
0 + 7.5x + x2 = 0 + 11
7.5x + x2 = 0 + 11

Combine like terms: 0 + 11 = 11
7.5x + x2 = 11

The x term is 7.5x.  Take half its coefficient (3.75).
Square it (14.0625) and add it to both sides.

Add '14.0625' to each side of the equation.
7.5x + 14.0625 + x2 = 11 + 14.0625

Reorder the terms:
14.0625 + 7.5x + x2 = 11 + 14.0625

Combine like terms: 11 + 14.0625 = 25.0625
14.0625 + 7.5x + x2 = 25.0625

Factor a perfect square on the left side:
(x + 3.75)(x + 3.75) = 25.0625

Calculate the square root of the right side: 5.006246099

Break this problem into two subproblems by setting 
(x + 3.75) equal to 5.006246099 and -5.006246099.


Subproblem 1
x + 3.75 = 5.006246099

Simplifying
x + 3.75 = 5.006246099

Reorder the terms:
3.75 + x = 5.006246099

Solving
3.75 + x = 5.006246099

Solving for variable 'x'.

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

Add '-3.75' to each side of the equation.
3.75 + -3.75 + x = 5.006246099 + -3.75

Combine like terms: 3.75 + -3.75 = 0.00
0.00 + x = 5.006246099 + -3.75
x = 5.006246099 + -3.75

Combine like terms: 5.006246099 + -3.75 = 1.256246099
x = 1.256246099

Simplifying
x = 1.256246099


Subproblem 2
x + 3.75 = -5.006246099

Simplifying
x + 3.75 = -5.006246099

Reorder the terms:
3.75 + x = -5.006246099

Solving
3.75 + x = -5.006246099

Solving for variable 'x'.

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

Add '-3.75' to each side of the equation.
3.75 + -3.75 + x = -5.006246099 + -3.75

Combine like terms: 3.75 + -3.75 = 0.00
0.00 + x = -5.006246099 + -3.75
x = -5.006246099 + -3.75

Combine like terms: -5.006246099 + -3.75 = -8.756246099
x = -8.756246099

Simplifying
x = -8.756246099


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.256246099, -8.756246099}
Solution
x = {1.256246099, -8.756246099}

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