x^2+9x-44=0

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


Simplifying
x2 + 9x + -44 = 0

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

Solving
-44 + 9x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '44' to each side of the equation.
-44 + 9x + 44 + x2 = 0 + 44

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

Combine like terms: -44 + 44 = 0
0 + 9x + x2 = 0 + 44
9x + x2 = 0 + 44

Combine like terms: 0 + 44 = 44
9x + x2 = 44

The x term is 9x.  Take half its coefficient (4.5).
Square it (20.25) and add it to both sides.

Add '20.25' to each side of the equation.
9x + 20.25 + x2 = 44 + 20.25

Reorder the terms:
20.25 + 9x + x2 = 44 + 20.25

Combine like terms: 44 + 20.25 = 64.25
20.25 + 9x + x2 = 64.25

Factor a perfect square on the left side:
(x + 4.5)(x + 4.5) = 64.25

Calculate the square root of the right side: 8.015609771

Break this problem into two subproblems by setting 
(x + 4.5) equal to 8.015609771 and -8.015609771.


Subproblem 1
x + 4.5 = 8.015609771

Simplifying
x + 4.5 = 8.015609771

Reorder the terms:
4.5 + x = 8.015609771

Solving
4.5 + x = 8.015609771

Solving for variable 'x'.

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

Add '-4.5' to each side of the equation.
4.5 + -4.5 + x = 8.015609771 + -4.5

Combine like terms: 4.5 + -4.5 = 0.0
0.0 + x = 8.015609771 + -4.5
x = 8.015609771 + -4.5

Combine like terms: 8.015609771 + -4.5 = 3.515609771
x = 3.515609771

Simplifying
x = 3.515609771


Subproblem 2
x + 4.5 = -8.015609771

Simplifying
x + 4.5 = -8.015609771

Reorder the terms:
4.5 + x = -8.015609771

Solving
4.5 + x = -8.015609771

Solving for variable 'x'.

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

Add '-4.5' to each side of the equation.
4.5 + -4.5 + x = -8.015609771 + -4.5

Combine like terms: 4.5 + -4.5 = 0.0
0.0 + x = -8.015609771 + -4.5
x = -8.015609771 + -4.5

Combine like terms: -8.015609771 + -4.5 = -12.515609771
x = -12.515609771

Simplifying
x = -12.515609771


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.515609771, -12.515609771}

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