0=x^2+40x+44

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Solution for 0=x^2+40x+44 equation: 


Simplifying
0 = x2 + 40x + 44

Reorder the terms:
0 = 44 + 40x + x2

Solving
0 = 44 + 40x + x2

Solving for variable 'x'.

Combine like terms: 0 + -44 = -44
-44 + -40x + -1x2 = 44 + 40x + x2 + -44 + -40x + -1x2

Reorder the terms:
-44 + -40x + -1x2 = 44 + -44 + 40x + -40x + x2 + -1x2

Combine like terms: 44 + -44 = 0
-44 + -40x + -1x2 = 0 + 40x + -40x + x2 + -1x2
-44 + -40x + -1x2 = 40x + -40x + x2 + -1x2

Combine like terms: 40x + -40x = 0
-44 + -40x + -1x2 = 0 + x2 + -1x2
-44 + -40x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-44 + -40x + -1x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(44 + 40x + x2) = 0

Ignore the factor -1.

Subproblem 1
Set the factor '(44 + 40x + x2)' equal to zero and attempt to solve:

Simplifying
44 + 40x + x2 = 0

Solving
44 + 40x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-44' to each side of the equation.
44 + 40x + -44 + x2 = 0 + -44

Reorder the terms:
44 + -44 + 40x + x2 = 0 + -44

Combine like terms: 44 + -44 = 0
0 + 40x + x2 = 0 + -44
40x + x2 = 0 + -44

Combine like terms: 0 + -44 = -44
40x + x2 = -44

The x term is 40x.  Take half its coefficient (20).
Square it (400) and add it to both sides.

Add '400' to each side of the equation.
40x + 400 + x2 = -44 + 400

Reorder the terms:
400 + 40x + x2 = -44 + 400

Combine like terms: -44 + 400 = 356
400 + 40x + x2 = 356

Factor a perfect square on the left side:
(x + 20)(x + 20) = 356

Calculate the square root of the right side: 18.867962264

Break this problem into two subproblems by setting 
(x + 20) equal to 18.867962264 and -18.867962264.


Subproblem 1
x + 20 = 18.867962264

Simplifying
x + 20 = 18.867962264

Reorder the terms:
20 + x = 18.867962264

Solving
20 + x = 18.867962264

Solving for variable 'x'.

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

Add '-20' to each side of the equation.
20 + -20 + x = 18.867962264 + -20

Combine like terms: 20 + -20 = 0
0 + x = 18.867962264 + -20
x = 18.867962264 + -20

Combine like terms: 18.867962264 + -20 = -1.132037736
x = -1.132037736

Simplifying
x = -1.132037736


Subproblem 2
x + 20 = -18.867962264

Simplifying
x + 20 = -18.867962264

Reorder the terms:
20 + x = -18.867962264

Solving
20 + x = -18.867962264

Solving for variable 'x'.

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

Add '-20' to each side of the equation.
20 + -20 + x = -18.867962264 + -20

Combine like terms: 20 + -20 = 0
0 + x = -18.867962264 + -20
x = -18.867962264 + -20

Combine like terms: -18.867962264 + -20 = -38.867962264
x = -38.867962264

Simplifying
x = -38.867962264


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-1.132037736, -38.867962264}
Solution
x = {-1.132037736, -38.867962264}

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