15x^2+28x-44=0

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Solution for 15x^2+28x-44=0 equation: 


Simplifying
15x2 + 28x + -44 = 0

Reorder the terms:
-44 + 28x + 15x2 = 0

Solving
-44 + 28x + 15x2 = 0

Solving for variable 'x'.

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

Divide each side by '15'.
-2.933333333 + 1.866666667x + x2 = 0

Move the constant term to the right:

Add '2.933333333' to each side of the equation.
-2.933333333 + 1.866666667x + 2.933333333 + x2 = 0 + 2.933333333

Reorder the terms:
-2.933333333 + 2.933333333 + 1.866666667x + x2 = 0 + 2.933333333

Combine like terms: -2.933333333 + 2.933333333 = 0.000000000
0.000000000 + 1.866666667x + x2 = 0 + 2.933333333
1.866666667x + x2 = 0 + 2.933333333

Combine like terms: 0 + 2.933333333 = 2.933333333
1.866666667x + x2 = 2.933333333

The x term is 1.866666667x.  Take half its coefficient (0.9333333335).
Square it (0.8711111114) and add it to both sides.

Add '0.8711111114' to each side of the equation.
1.866666667x + 0.8711111114 + x2 = 2.933333333 + 0.8711111114

Reorder the terms:
0.8711111114 + 1.866666667x + x2 = 2.933333333 + 0.8711111114

Combine like terms: 2.933333333 + 0.8711111114 = 3.8044444444
0.8711111114 + 1.866666667x + x2 = 3.8044444444

Factor a perfect square on the left side:
(x + 0.9333333335)(x + 0.9333333335) = 3.8044444444

Calculate the square root of the right side: 1.950498512

Break this problem into two subproblems by setting 
(x + 0.9333333335) equal to 1.950498512 and -1.950498512.


Subproblem 1
x + 0.9333333335 = 1.950498512

Simplifying
x + 0.9333333335 = 1.950498512

Reorder the terms:
0.9333333335 + x = 1.950498512

Solving
0.9333333335 + x = 1.950498512

Solving for variable 'x'.

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

Add '-0.9333333335' to each side of the equation.
0.9333333335 + -0.9333333335 + x = 1.950498512 + -0.9333333335

Combine like terms: 0.9333333335 + -0.9333333335 = 0.0000000000
0.0000000000 + x = 1.950498512 + -0.9333333335
x = 1.950498512 + -0.9333333335

Combine like terms: 1.950498512 + -0.9333333335 = 1.0171651785
x = 1.0171651785

Simplifying
x = 1.0171651785


Subproblem 2
x + 0.9333333335 = -1.950498512

Simplifying
x + 0.9333333335 = -1.950498512

Reorder the terms:
0.9333333335 + x = -1.950498512

Solving
0.9333333335 + x = -1.950498512

Solving for variable 'x'.

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

Add '-0.9333333335' to each side of the equation.
0.9333333335 + -0.9333333335 + x = -1.950498512 + -0.9333333335

Combine like terms: 0.9333333335 + -0.9333333335 = 0.0000000000
0.0000000000 + x = -1.950498512 + -0.9333333335
x = -1.950498512 + -0.9333333335

Combine like terms: -1.950498512 + -0.9333333335 = -2.8838318455
x = -2.8838318455

Simplifying
x = -2.8838318455


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.0171651785, -2.8838318455}

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