x^2-0.9x=-0.18

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Solution for x^2-0.9x=-0.18 equation: 


Simplifying
x2 + -0.9x = -0.18

Reorder the terms:
-0.9x + x2 = -0.18

Solving
-0.9x + x2 = -0.18

Solving for variable 'x'.

Reorder the terms:
0.18 + -0.9x + x2 = -0.18 + 0.18

Combine like terms: -0.18 + 0.18 = 0.00
0.18 + -0.9x + x2 = 0.00

Begin completing the square.

Move the constant term to the right:

Add '-0.18' to each side of the equation.
0.18 + -0.9x + -0.18 + x2 = 0.00 + -0.18

Reorder the terms:
0.18 + -0.18 + -0.9x + x2 = 0.00 + -0.18

Combine like terms: 0.18 + -0.18 = 0.00
0.00 + -0.9x + x2 = 0.00 + -0.18
-0.9x + x2 = 0.00 + -0.18

Combine like terms: 0.00 + -0.18 = -0.18
-0.9x + x2 = -0.18

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 = -0.18 + 0.2025

Reorder the terms:
0.2025 + -0.9x + x2 = -0.18 + 0.2025

Combine like terms: -0.18 + 0.2025 = 0.0225
0.2025 + -0.9x + x2 = 0.0225

Factor a perfect square on the left side:
(x + -0.45)(x + -0.45) = 0.0225

Calculate the square root of the right side: 0.15

Break this problem into two subproblems by setting 
(x + -0.45) equal to 0.15 and -0.15.


Subproblem 1
x + -0.45 = 0.15

Simplifying
x + -0.45 = 0.15

Reorder the terms:
-0.45 + x = 0.15

Solving
-0.45 + x = 0.15

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 = 0.15 + 0.45

Combine like terms: -0.45 + 0.45 = 0.00
0.00 + x = 0.15 + 0.45
x = 0.15 + 0.45

Combine like terms: 0.15 + 0.45 = 0.6
x = 0.6

Simplifying
x = 0.6


Subproblem 2
x + -0.45 = -0.15

Simplifying
x + -0.45 = -0.15

Reorder the terms:
-0.45 + x = -0.15

Solving
-0.45 + x = -0.15

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 = -0.15 + 0.45

Combine like terms: -0.45 + 0.45 = 0.00
0.00 + x = -0.15 + 0.45
x = -0.15 + 0.45

Combine like terms: -0.15 + 0.45 = 0.3
x = 0.3

Simplifying
x = 0.3


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.6, 0.3}

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