9x^2-2.1x+0.1=0

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Solution for 9x^2-2.1x+0.1=0 equation:


Simplifying
9x2 + -2.1x + 0.1 = 0

Reorder the terms:
0.1 + -2.1x + 9x2 = 0

Solving
0.1 + -2.1x + 9x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
9 the coefficient of the squared term: 

Divide each side by '9'.
0.01111111111 + -0.2333333333x + x2 = 0

Move the constant term to the right:

Add '-0.01111111111' to each side of the equation.
0.01111111111 + -0.2333333333x + -0.01111111111 + x2 = 0 + -0.01111111111

Reorder the terms:
0.01111111111 + -0.01111111111 + -0.2333333333x + x2 = 0 + -0.01111111111

Combine like terms: 0.01111111111 + -0.01111111111 = 0.00000000000
0.00000000000 + -0.2333333333x + x2 = 0 + -0.01111111111
-0.2333333333x + x2 = 0 + -0.01111111111

Combine like terms: 0 + -0.01111111111 = -0.01111111111
-0.2333333333x + x2 = -0.01111111111

The x term is -0.2333333333x.  Take half its coefficient (-0.1166666667).
Square it (0.01361111112) and add it to both sides.

Add '0.01361111112' to each side of the equation.
-0.2333333333x + 0.01361111112 + x2 = -0.01111111111 + 0.01361111112

Reorder the terms:
0.01361111112 + -0.2333333333x + x2 = -0.01111111111 + 0.01361111112

Combine like terms: -0.01111111111 + 0.01361111112 = 0.00250000001
0.01361111112 + -0.2333333333x + x2 = 0.00250000001

Factor a perfect square on the left side:
(x + -0.1166666667)(x + -0.1166666667) = 0.00250000001

Calculate the square root of the right side: 0.05

Break this problem into two subproblems by setting 
(x + -0.1166666667) equal to 0.05 and -0.05.


Subproblem 1
x + -0.1166666667 = 0.05

Simplifying
x + -0.1166666667 = 0.05

Reorder the terms:
-0.1166666667 + x = 0.05

Solving
-0.1166666667 + x = 0.05

Solving for variable 'x'.

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

Add '0.1166666667' to each side of the equation.
-0.1166666667 + 0.1166666667 + x = 0.05 + 0.1166666667

Combine like terms: -0.1166666667 + 0.1166666667 = 0.0000000000
0.0000000000 + x = 0.05 + 0.1166666667
x = 0.05 + 0.1166666667

Combine like terms: 0.05 + 0.1166666667 = 0.1666666667
x = 0.1666666667

Simplifying
x = 0.1666666667


Subproblem 2
x + -0.1166666667 = -0.05

Simplifying
x + -0.1166666667 = -0.05

Reorder the terms:
-0.1166666667 + x = -0.05

Solving
-0.1166666667 + x = -0.05

Solving for variable 'x'.

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

Add '0.1166666667' to each side of the equation.
-0.1166666667 + 0.1166666667 + x = -0.05 + 0.1166666667

Combine like terms: -0.1166666667 + 0.1166666667 = 0.0000000000
0.0000000000 + x = -0.05 + 0.1166666667
x = -0.05 + 0.1166666667

Combine like terms: -0.05 + 0.1166666667 = 0.0666666667
x = 0.0666666667

Simplifying
x = 0.0666666667


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.1666666667, 0.0666666667}

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