x^2+44x+-40=0

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


Simplifying
x2 + 44x + -40 = 0

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

Solving
-40 + 44x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

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

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

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

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

The x term is 44x.  Take half its coefficient (22).
Square it (484) and add it to both sides.

Add '484' to each side of the equation.
44x + 484 + x2 = 40 + 484

Reorder the terms:
484 + 44x + x2 = 40 + 484

Combine like terms: 40 + 484 = 524
484 + 44x + x2 = 524

Factor a perfect square on the left side:
(x + 22)(x + 22) = 524

Calculate the square root of the right side: 22.891046285

Break this problem into two subproblems by setting 
(x + 22) equal to 22.891046285 and -22.891046285.


Subproblem 1
x + 22 = 22.891046285

Simplifying
x + 22 = 22.891046285

Reorder the terms:
22 + x = 22.891046285

Solving
22 + x = 22.891046285

Solving for variable 'x'.

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

Add '-22' to each side of the equation.
22 + -22 + x = 22.891046285 + -22

Combine like terms: 22 + -22 = 0
0 + x = 22.891046285 + -22
x = 22.891046285 + -22

Combine like terms: 22.891046285 + -22 = 0.891046285
x = 0.891046285

Simplifying
x = 0.891046285


Subproblem 2
x + 22 = -22.891046285

Simplifying
x + 22 = -22.891046285

Reorder the terms:
22 + x = -22.891046285

Solving
22 + x = -22.891046285

Solving for variable 'x'.

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

Add '-22' to each side of the equation.
22 + -22 + x = -22.891046285 + -22

Combine like terms: 22 + -22 = 0
0 + x = -22.891046285 + -22
x = -22.891046285 + -22

Combine like terms: -22.891046285 + -22 = -44.891046285
x = -44.891046285

Simplifying
x = -44.891046285


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.891046285, -44.891046285}

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