x^2-0.9x-0.2=0

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Solution for x^2-0.9x-0.2=0 equation: 


Simplifying
x2 + -0.9x + -0.2 = 0

Reorder the terms:
-0.2 + -0.9x + x2 = 0

Solving
-0.2 + -0.9x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '0.2' to each side of the equation.
-0.2 + -0.9x + 0.2 + x2 = 0 + 0.2

Reorder the terms:
-0.2 + 0.2 + -0.9x + x2 = 0 + 0.2

Combine like terms: -0.2 + 0.2 = 0.0
0.0 + -0.9x + x2 = 0 + 0.2
-0.9x + x2 = 0 + 0.2

Combine like terms: 0 + 0.2 = 0.2
-0.9x + x2 = 0.2

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 = 0.2 + 0.2025

Reorder the terms:
0.2025 + -0.9x + x2 = 0.2 + 0.2025

Combine like terms: 0.2 + 0.2025 = 0.4025
0.2025 + -0.9x + x2 = 0.4025

Factor a perfect square on the left side:
(x + -0.45)(x + -0.45) = 0.4025

Calculate the square root of the right side: 0.634428877

Break this problem into two subproblems by setting 
(x + -0.45) equal to 0.634428877 and -0.634428877.


Subproblem 1
x + -0.45 = 0.634428877

Simplifying
x + -0.45 = 0.634428877

Reorder the terms:
-0.45 + x = 0.634428877

Solving
-0.45 + x = 0.634428877

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 = 0.634428877 + 0.45

Combine like terms: -0.45 + 0.45 = 0.00
0.00 + x = 0.634428877 + 0.45
x = 0.634428877 + 0.45

Combine like terms: 0.634428877 + 0.45 = 1.084428877
x = 1.084428877

Simplifying
x = 1.084428877


Subproblem 2
x + -0.45 = -0.634428877

Simplifying
x + -0.45 = -0.634428877

Reorder the terms:
-0.45 + x = -0.634428877

Solving
-0.45 + x = -0.634428877

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 = -0.634428877 + 0.45

Combine like terms: -0.45 + 0.45 = 0.00
0.00 + x = -0.634428877 + 0.45
x = -0.634428877 + 0.45

Combine like terms: -0.634428877 + 0.45 = -0.184428877
x = -0.184428877

Simplifying
x = -0.184428877


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.084428877, -0.184428877}

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