5x^2+18x-44=0

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Solution for 5x^2+18x-44=0 equation: 


Simplifying
5x2 + 18x + -44 = 0

Reorder the terms:
-44 + 18x + 5x2 = 0

Solving
-44 + 18x + 5x2 = 0

Solving for variable 'x'.

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

Divide each side by '5'.
-8.8 + 3.6x + x2 = 0

Move the constant term to the right:

Add '8.8' to each side of the equation.
-8.8 + 3.6x + 8.8 + x2 = 0 + 8.8

Reorder the terms:
-8.8 + 8.8 + 3.6x + x2 = 0 + 8.8

Combine like terms: -8.8 + 8.8 = 0.0
0.0 + 3.6x + x2 = 0 + 8.8
3.6x + x2 = 0 + 8.8

Combine like terms: 0 + 8.8 = 8.8
3.6x + x2 = 8.8

The x term is 3.6x.  Take half its coefficient (1.8).
Square it (3.24) and add it to both sides.

Add '3.24' to each side of the equation.
3.6x + 3.24 + x2 = 8.8 + 3.24

Reorder the terms:
3.24 + 3.6x + x2 = 8.8 + 3.24

Combine like terms: 8.8 + 3.24 = 12.04
3.24 + 3.6x + x2 = 12.04

Factor a perfect square on the left side:
(x + 1.8)(x + 1.8) = 12.04

Calculate the square root of the right side: 3.469870315

Break this problem into two subproblems by setting 
(x + 1.8) equal to 3.469870315 and -3.469870315.


Subproblem 1
x + 1.8 = 3.469870315

Simplifying
x + 1.8 = 3.469870315

Reorder the terms:
1.8 + x = 3.469870315

Solving
1.8 + x = 3.469870315

Solving for variable 'x'.

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

Add '-1.8' to each side of the equation.
1.8 + -1.8 + x = 3.469870315 + -1.8

Combine like terms: 1.8 + -1.8 = 0.0
0.0 + x = 3.469870315 + -1.8
x = 3.469870315 + -1.8

Combine like terms: 3.469870315 + -1.8 = 1.669870315
x = 1.669870315

Simplifying
x = 1.669870315


Subproblem 2
x + 1.8 = -3.469870315

Simplifying
x + 1.8 = -3.469870315

Reorder the terms:
1.8 + x = -3.469870315

Solving
1.8 + x = -3.469870315

Solving for variable 'x'.

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

Add '-1.8' to each side of the equation.
1.8 + -1.8 + x = -3.469870315 + -1.8

Combine like terms: 1.8 + -1.8 = 0.0
0.0 + x = -3.469870315 + -1.8
x = -3.469870315 + -1.8

Combine like terms: -3.469870315 + -1.8 = -5.269870315
x = -5.269870315

Simplifying
x = -5.269870315


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.669870315, -5.269870315}

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