-5x^2-44x-9=0

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Solution for -5x^2-44x-9=0 equation: 


Simplifying
-5x2 + -44x + -9 = 0

Reorder the terms:
-9 + -44x + -5x2 = 0

Solving
-9 + -44x + -5x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '-1'.
-1(9 + 44x + 5x2) = 0

Ignore the factor -1.

Subproblem 1
Set the factor '(9 + 44x + 5x2)' equal to zero and attempt to solve:

Simplifying
9 + 44x + 5x2 = 0

Solving
9 + 44x + 5x2 = 0

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

Divide each side by '5'.
1.8 + 8.8x + x2 = 0

Move the constant term to the right:

Add '-1.8' to each side of the equation.
1.8 + 8.8x + -1.8 + x2 = 0 + -1.8

Reorder the terms:
1.8 + -1.8 + 8.8x + x2 = 0 + -1.8

Combine like terms: 1.8 + -1.8 = 0.0
0.0 + 8.8x + x2 = 0 + -1.8
8.8x + x2 = 0 + -1.8

Combine like terms: 0 + -1.8 = -1.8
8.8x + x2 = -1.8

The x term is 8.8x.  Take half its coefficient (4.4).
Square it (19.36) and add it to both sides.

Add '19.36' to each side of the equation.
8.8x + 19.36 + x2 = -1.8 + 19.36

Reorder the terms:
19.36 + 8.8x + x2 = -1.8 + 19.36

Combine like terms: -1.8 + 19.36 = 17.56
19.36 + 8.8x + x2 = 17.56

Factor a perfect square on the left side:
(x + 4.4)(x + 4.4) = 17.56

Calculate the square root of the right side: 4.190465368

Break this problem into two subproblems by setting 
(x + 4.4) equal to 4.190465368 and -4.190465368.


Subproblem 1
x + 4.4 = 4.190465368

Simplifying
x + 4.4 = 4.190465368

Reorder the terms:
4.4 + x = 4.190465368

Solving
4.4 + x = 4.190465368

Solving for variable 'x'.

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

Add '-4.4' to each side of the equation.
4.4 + -4.4 + x = 4.190465368 + -4.4

Combine like terms: 4.4 + -4.4 = 0.0
0.0 + x = 4.190465368 + -4.4
x = 4.190465368 + -4.4

Combine like terms: 4.190465368 + -4.4 = -0.209534632
x = -0.209534632

Simplifying
x = -0.209534632


Subproblem 2
x + 4.4 = -4.190465368

Simplifying
x + 4.4 = -4.190465368

Reorder the terms:
4.4 + x = -4.190465368

Solving
4.4 + x = -4.190465368

Solving for variable 'x'.

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

Add '-4.4' to each side of the equation.
4.4 + -4.4 + x = -4.190465368 + -4.4

Combine like terms: 4.4 + -4.4 = 0.0
0.0 + x = -4.190465368 + -4.4
x = -4.190465368 + -4.4

Combine like terms: -4.190465368 + -4.4 = -8.590465368
x = -8.590465368

Simplifying
x = -8.590465368


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.209534632, -8.590465368}
Solution
x = {-0.209534632, -8.590465368}

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