x^2-0.9x+0.2=3

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Solution for x^2-0.9x+0.2=3 equation: 


Simplifying
x2 + -0.9x + 0.2 = 3

Reorder the terms:
0.2 + -0.9x + x2 = 3

Solving
0.2 + -0.9x + x2 = 3

Solving for variable 'x'.

Reorder the terms:
0.2 + -3 + -0.9x + x2 = 3 + -3

Combine like terms: 0.2 + -3 = -2.8
-2.8 + -0.9x + x2 = 3 + -3

Combine like terms: 3 + -3 = 0
-2.8 + -0.9x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '2.8' to each side of the equation.
-2.8 + -0.9x + 2.8 + x2 = 0 + 2.8

Reorder the terms:
-2.8 + 2.8 + -0.9x + x2 = 0 + 2.8

Combine like terms: -2.8 + 2.8 = 0.0
0.0 + -0.9x + x2 = 0 + 2.8
-0.9x + x2 = 0 + 2.8

Combine like terms: 0 + 2.8 = 2.8
-0.9x + x2 = 2.8

The x term is -0.9x.  Take half its coefficient (-0.45).
Square it (0.2025) and add it to both sides.

Add '0.2025' to each side of the equation.
-0.9x + 0.2025 + x2 = 2.8 + 0.2025

Reorder the terms:
0.2025 + -0.9x + x2 = 2.8 + 0.2025

Combine like terms: 2.8 + 0.2025 = 3.0025
0.2025 + -0.9x + x2 = 3.0025

Factor a perfect square on the left side:
(x + -0.45)(x + -0.45) = 3.0025

Calculate the square root of the right side: 1.732772345

Break this problem into two subproblems by setting 
(x + -0.45) equal to 1.732772345 and -1.732772345.


Subproblem 1
x + -0.45 = 1.732772345

Simplifying
x + -0.45 = 1.732772345

Reorder the terms:
-0.45 + x = 1.732772345

Solving
-0.45 + x = 1.732772345

Solving for variable 'x'.

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

Add '0.45' to each side of the equation.
-0.45 + 0.45 + x = 1.732772345 + 0.45

Combine like terms: -0.45 + 0.45 = 0.00
0.00 + x = 1.732772345 + 0.45
x = 1.732772345 + 0.45

Combine like terms: 1.732772345 + 0.45 = 2.182772345
x = 2.182772345

Simplifying
x = 2.182772345


Subproblem 2
x + -0.45 = -1.732772345

Simplifying
x + -0.45 = -1.732772345

Reorder the terms:
-0.45 + x = -1.732772345

Solving
-0.45 + x = -1.732772345

Solving for variable 'x'.

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

Add '0.45' to each side of the equation.
-0.45 + 0.45 + x = -1.732772345 + 0.45

Combine like terms: -0.45 + 0.45 = 0.00
0.00 + x = -1.732772345 + 0.45
x = -1.732772345 + 0.45

Combine like terms: -1.732772345 + 0.45 = -1.282772345
x = -1.282772345

Simplifying
x = -1.282772345


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.182772345, -1.282772345}

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