x^2+.44x-.11=0

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Solution for x^2+.44x-.11=0 equation: 


Simplifying
x2 + 0.44x + -0.11 = 0

Reorder the terms:
-0.11 + 0.44x + x2 = 0

Solving
-0.11 + 0.44x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '0.11' to each side of the equation.
-0.11 + 0.44x + 0.11 + x2 = 0 + 0.11

Reorder the terms:
-0.11 + 0.11 + 0.44x + x2 = 0 + 0.11

Combine like terms: -0.11 + 0.11 = 0.00
0.00 + 0.44x + x2 = 0 + 0.11
0.44x + x2 = 0 + 0.11

Combine like terms: 0 + 0.11 = 0.11
0.44x + x2 = 0.11

The x term is 0.44x.  Take half its coefficient (0.22).
Square it (0.0484) and add it to both sides.

Add '0.0484' to each side of the equation.
0.44x + 0.0484 + x2 = 0.11 + 0.0484

Reorder the terms:
0.0484 + 0.44x + x2 = 0.11 + 0.0484

Combine like terms: 0.11 + 0.0484 = 0.1584
0.0484 + 0.44x + x2 = 0.1584

Factor a perfect square on the left side:
(x + 0.22)(x + 0.22) = 0.1584

Calculate the square root of the right side: 0.397994975

Break this problem into two subproblems by setting 
(x + 0.22) equal to 0.397994975 and -0.397994975.


Subproblem 1
x + 0.22 = 0.397994975

Simplifying
x + 0.22 = 0.397994975

Reorder the terms:
0.22 + x = 0.397994975

Solving
0.22 + x = 0.397994975

Solving for variable 'x'.

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

Add '-0.22' to each side of the equation.
0.22 + -0.22 + x = 0.397994975 + -0.22

Combine like terms: 0.22 + -0.22 = 0.00
0.00 + x = 0.397994975 + -0.22
x = 0.397994975 + -0.22

Combine like terms: 0.397994975 + -0.22 = 0.177994975
x = 0.177994975

Simplifying
x = 0.177994975


Subproblem 2
x + 0.22 = -0.397994975

Simplifying
x + 0.22 = -0.397994975

Reorder the terms:
0.22 + x = -0.397994975

Solving
0.22 + x = -0.397994975

Solving for variable 'x'.

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

Add '-0.22' to each side of the equation.
0.22 + -0.22 + x = -0.397994975 + -0.22

Combine like terms: 0.22 + -0.22 = 0.00
0.00 + x = -0.397994975 + -0.22
x = -0.397994975 + -0.22

Combine like terms: -0.397994975 + -0.22 = -0.617994975
x = -0.617994975

Simplifying
x = -0.617994975


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.177994975, -0.617994975}

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