x^2+4.4x=4.16

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Solution for x^2+4.4x=4.16 equation: 


Simplifying
x2 + 4.4x = 4.16

Reorder the terms:
4.4x + x2 = 4.16

Solving
4.4x + x2 = 4.16

Solving for variable 'x'.

Reorder the terms:
-4.16 + 4.4x + x2 = 4.16 + -4.16

Combine like terms: 4.16 + -4.16 = 0.00
-4.16 + 4.4x + x2 = 0.00

Begin completing the square.

Move the constant term to the right:

Add '4.16' to each side of the equation.
-4.16 + 4.4x + 4.16 + x2 = 0.00 + 4.16

Reorder the terms:
-4.16 + 4.16 + 4.4x + x2 = 0.00 + 4.16

Combine like terms: -4.16 + 4.16 = 0.00
0.00 + 4.4x + x2 = 0.00 + 4.16
4.4x + x2 = 0.00 + 4.16

Combine like terms: 0.00 + 4.16 = 4.16
4.4x + x2 = 4.16

The x term is 4.4x.  Take half its coefficient (2.2).
Square it (4.84) and add it to both sides.

Add '4.84' to each side of the equation.
4.4x + 4.84 + x2 = 4.16 + 4.84

Reorder the terms:
4.84 + 4.4x + x2 = 4.16 + 4.84

Combine like terms: 4.16 + 4.84 = 9
4.84 + 4.4x + x2 = 9

Factor a perfect square on the left side:
(x + 2.2)(x + 2.2) = 9

Calculate the square root of the right side: 3

Break this problem into two subproblems by setting 
(x + 2.2) equal to 3 and -3.


Subproblem 1
x + 2.2 = 3

Simplifying
x + 2.2 = 3

Reorder the terms:
2.2 + x = 3

Solving
2.2 + x = 3

Solving for variable 'x'.

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

Add '-2.2' to each side of the equation.
2.2 + -2.2 + x = 3 + -2.2

Combine like terms: 2.2 + -2.2 = 0.0
0.0 + x = 3 + -2.2
x = 3 + -2.2

Combine like terms: 3 + -2.2 = 0.8
x = 0.8

Simplifying
x = 0.8


Subproblem 2
x + 2.2 = -3

Simplifying
x + 2.2 = -3

Reorder the terms:
2.2 + x = -3

Solving
2.2 + x = -3

Solving for variable 'x'.

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

Add '-2.2' to each side of the equation.
2.2 + -2.2 + x = -3 + -2.2

Combine like terms: 2.2 + -2.2 = 0.0
0.0 + x = -3 + -2.2
x = -3 + -2.2

Combine like terms: -3 + -2.2 = -5.2
x = -5.2

Simplifying
x = -5.2


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.8, -5.2}

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