x^2-4.43x-22.55=0

Solution for x^2-4.43x-22.55=0 equation:

Simplifying
x2 + -4.43x + -22.55 = 0

Reorder the terms:
-22.55 + -4.43x + x2 = 0

Solving
-22.55 + -4.43x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '22.55' to each side of the equation.
-22.55 + -4.43x + 22.55 + x2 = 0 + 22.55

Reorder the terms:
-22.55 + 22.55 + -4.43x + x2 = 0 + 22.55

Combine like terms: -22.55 + 22.55 = 0.00
0.00 + -4.43x + x2 = 0 + 22.55
-4.43x + x2 = 0 + 22.55

Combine like terms: 0 + 22.55 = 22.55
-4.43x + x2 = 22.55

The x term is -4.43x.  Take half its coefficient (-2.215).
Square it (4.906225) and add it to both sides.

Add '4.906225' to each side of the equation.
-4.43x + 4.906225 + x2 = 22.55 + 4.906225

Reorder the terms:
4.906225 + -4.43x + x2 = 22.55 + 4.906225

Combine like terms: 22.55 + 4.906225 = 27.456225
4.906225 + -4.43x + x2 = 27.456225

Factor a perfect square on the left side:
(x + -2.215)(x + -2.215) = 27.456225

Calculate the square root of the right side: 5.239868796

Break this problem into two subproblems by setting 
(x + -2.215) equal to 5.239868796 and -5.239868796.

Subproblem 1
x + -2.215 = 5.239868796

Simplifying
x + -2.215 = 5.239868796

Reorder the terms:
-2.215 + x = 5.239868796

Solving
-2.215 + x = 5.239868796

Solving for variable 'x'.

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

Add '2.215' to each side of the equation.
-2.215 + 2.215 + x = 5.239868796 + 2.215

Combine like terms: -2.215 + 2.215 = 0.000
0.000 + x = 5.239868796 + 2.215
x = 5.239868796 + 2.215

Combine like terms: 5.239868796 + 2.215 = 7.454868796
x = 7.454868796

Simplifying
x = 7.454868796

Subproblem 2
x + -2.215 = -5.239868796

Simplifying
x + -2.215 = -5.239868796

Reorder the terms:
-2.215 + x = -5.239868796

Solving
-2.215 + x = -5.239868796

Solving for variable 'x'.

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

Add '2.215' to each side of the equation.
-2.215 + 2.215 + x = -5.239868796 + 2.215

Combine like terms: -2.215 + 2.215 = 0.000
0.000 + x = -5.239868796 + 2.215
x = -5.239868796 + 2.215

Combine like terms: -5.239868796 + 2.215 = -3.024868796
x = -3.024868796

Simplifying
x = -3.024868796

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {7.454868796, -3.024868796}