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Simplifying
100x2 + -100x + 9 = 0

Reorder the terms:
9 + -100x + 100x2 = 0

Solving
9 + -100x + 100x2 = 0

Solving for variable 'x'.

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

Divide each side by '100'.
0.09 + -1x + x2 = 0

Move the constant term to the right:

Add '-0.09' to each side of the equation.
0.09 + -1x + -0.09 + x2 = 0 + -0.09

Reorder the terms:
0.09 + -0.09 + -1x + x2 = 0 + -0.09

Combine like terms: 0.09 + -0.09 = 0.00
0.00 + -1x + x2 = 0 + -0.09
-1x + x2 = 0 + -0.09

Combine like terms: 0 + -0.09 = -0.09
-1x + x2 = -0.09

The x term is -1x.  Take half its coefficient (-0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-1x + 0.25 + x2 = -0.09 + 0.25

Reorder the terms:
0.25 + -1x + x2 = -0.09 + 0.25

Combine like terms: -0.09 + 0.25 = 0.16
0.25 + -1x + x2 = 0.16

Factor a perfect square on the left side:
(x + -0.5)(x + -0.5) = 0.16

Calculate the square root of the right side: 0.4

Break this problem into two subproblems by setting 
(x + -0.5) equal to 0.4 and -0.4.

Subproblem 1

x + -0.5 = 0.4 Simplifying x + -0.5 = 0.4 Reorder the terms: -0.5 + x = 0.4 Solving -0.5 + x = 0.4 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = 0.4 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 0.4 + 0.5 x = 0.4 + 0.5 Combine like terms: 0.4 + 0.5 = 0.9 x = 0.9 Simplifying x = 0.9

Subproblem 2

x + -0.5 = -0.4 Simplifying x + -0.5 = -0.4 Reorder the terms: -0.5 + x = -0.4 Solving -0.5 + x = -0.4 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = -0.4 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -0.4 + 0.5 x = -0.4 + 0.5 Combine like terms: -0.4 + 0.5 = 0.1 x = 0.1 Simplifying x = 0.1

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.9, 0.1}
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