x^2-2x=1.1

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Solution for x^2-2x=1.1 equation: 


Simplifying
x2 + -2x = 1.1

Reorder the terms:
-2x + x2 = 1.1

Solving
-2x + x2 = 1.1

Solving for variable 'x'.

Reorder the terms:
-1.1 + -2x + x2 = 1.1 + -1.1

Combine like terms: 1.1 + -1.1 = 0.0
-1.1 + -2x + x2 = 0.0

Begin completing the square.

Move the constant term to the right:

Add '1.1' to each side of the equation.
-1.1 + -2x + 1.1 + x2 = 0.0 + 1.1

Reorder the terms:
-1.1 + 1.1 + -2x + x2 = 0.0 + 1.1

Combine like terms: -1.1 + 1.1 = 0.0
0.0 + -2x + x2 = 0.0 + 1.1
-2x + x2 = 0.0 + 1.1

Combine like terms: 0.0 + 1.1 = 1.1
-2x + x2 = 1.1

The x term is -2x.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2x + 1 + x2 = 1.1 + 1

Reorder the terms:
1 + -2x + x2 = 1.1 + 1

Combine like terms: 1.1 + 1 = 2.1
1 + -2x + x2 = 2.1

Factor a perfect square on the left side:
(x + -1)(x + -1) = 2.1

Calculate the square root of the right side: 1.449137675

Break this problem into two subproblems by setting 
(x + -1) equal to 1.449137675 and -1.449137675.


Subproblem 1
x + -1 = 1.449137675

Simplifying
x + -1 = 1.449137675

Reorder the terms:
-1 + x = 1.449137675

Solving
-1 + x = 1.449137675

Solving for variable 'x'.

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

Add '1' to each side of the equation.
-1 + 1 + x = 1.449137675 + 1

Combine like terms: -1 + 1 = 0
0 + x = 1.449137675 + 1
x = 1.449137675 + 1

Combine like terms: 1.449137675 + 1 = 2.449137675
x = 2.449137675

Simplifying
x = 2.449137675


Subproblem 2
x + -1 = -1.449137675

Simplifying
x + -1 = -1.449137675

Reorder the terms:
-1 + x = -1.449137675

Solving
-1 + x = -1.449137675

Solving for variable 'x'.

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

Add '1' to each side of the equation.
-1 + 1 + x = -1.449137675 + 1

Combine like terms: -1 + 1 = 0
0 + x = -1.449137675 + 1
x = -1.449137675 + 1

Combine like terms: -1.449137675 + 1 = -0.449137675
x = -0.449137675

Simplifying
x = -0.449137675


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.449137675, -0.449137675}

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