9x^2-0.6x+0.01=

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Solution for 9x^2-0.6x+0.01= equation: 


Simplifying
9x2 + -0.6x + 0.01 = 0

Reorder the terms:
0.01 + -0.6x + 9x2 = 0

Solving
0.01 + -0.6x + 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'.
0.001111111111 + -0.06666666667x + x2 = 0

Move the constant term to the right:

Add '-0.001111111111' to each side of the equation.
0.001111111111 + -0.06666666667x + -0.001111111111 + x2 = 0 + -0.001111111111

Reorder the terms:
0.001111111111 + -0.001111111111 + -0.06666666667x + x2 = 0 + -0.001111111111

Combine like terms: 0.001111111111 + -0.001111111111 = 0.000000000000
0.000000000000 + -0.06666666667x + x2 = 0 + -0.001111111111
-0.06666666667x + x2 = 0 + -0.001111111111

Combine like terms: 0 + -0.001111111111 = -0.001111111111
-0.06666666667x + x2 = -0.001111111111

The x term is -0.06666666667x.  Take half its coefficient (-0.03333333334).
Square it (0.001111111112) and add it to both sides.

Add '0.001111111112' to each side of the equation.
-0.06666666667x + 0.001111111112 + x2 = -0.001111111111 + 0.001111111112

Reorder the terms:
0.001111111112 + -0.06666666667x + x2 = -0.001111111111 + 0.001111111112

Combine like terms: -0.001111111111 + 0.001111111112 = 0.000000000001
0.001111111112 + -0.06666666667x + x2 = 0.000000000001

Factor a perfect square on the left side:
(x + -0.03333333334)(x + -0.03333333334) = 0.000000000001

Calculate the square root of the right side: 0.000001

Break this problem into two subproblems by setting 
(x + -0.03333333334) equal to 0.000001 and -0.000001.


Subproblem 1
x + -0.03333333334 = 0.000001

Simplifying
x + -0.03333333334 = 0.000001

Reorder the terms:
-0.03333333334 + x = 0.000001

Solving
-0.03333333334 + x = 0.000001

Solving for variable 'x'.

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

Add '0.03333333334' to each side of the equation.
-0.03333333334 + 0.03333333334 + x = 0.000001 + 0.03333333334

Combine like terms: -0.03333333334 + 0.03333333334 = 0.00000000000
0.00000000000 + x = 0.000001 + 0.03333333334
x = 0.000001 + 0.03333333334

Combine like terms: 0.000001 + 0.03333333334 = 0.03333433334
x = 0.03333433334

Simplifying
x = 0.03333433334


Subproblem 2
x + -0.03333333334 = -0.000001

Simplifying
x + -0.03333333334 = -0.000001

Reorder the terms:
-0.03333333334 + x = -0.000001

Solving
-0.03333333334 + x = -0.000001

Solving for variable 'x'.

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

Add '0.03333333334' to each side of the equation.
-0.03333333334 + 0.03333333334 + x = -0.000001 + 0.03333333334

Combine like terms: -0.03333333334 + 0.03333333334 = 0.00000000000
0.00000000000 + x = -0.000001 + 0.03333333334
x = -0.000001 + 0.03333333334

Combine like terms: -0.000001 + 0.03333333334 = 0.03333233334
x = 0.03333233334

Simplifying
x = 0.03333233334


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.03333433334, 0.03333233334}

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