3x^2-0.2x+0.0024=0

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Solution for 3x^2-0.2x+0.0024=0 equation:


Simplifying
3x2 + -0.2x + 0.0024 = 0

Reorder the terms:
0.0024 + -0.2x + 3x2 = 0

Solving
0.0024 + -0.2x + 3x2 = 0

Solving for variable 'x'.

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

Divide each side by '3'.
0.0008 + -0.06666666667x + x2 = 0

Move the constant term to the right:

Add '-0.0008' to each side of the equation.
0.0008 + -0.06666666667x + -0.0008 + x2 = 0 + -0.0008

Reorder the terms:
0.0008 + -0.0008 + -0.06666666667x + x2 = 0 + -0.0008

Combine like terms: 0.0008 + -0.0008 = 0.0000
0.0000 + -0.06666666667x + x2 = 0 + -0.0008
-0.06666666667x + x2 = 0 + -0.0008

Combine like terms: 0 + -0.0008 = -0.0008
-0.06666666667x + x2 = -0.0008

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 = -0.0008 + 0.001111111112

Reorder the terms:
0.001111111112 + -0.06666666667x + x2 = -0.0008 + 0.001111111112

Combine like terms: -0.0008 + 0.001111111112 = 0.000311111112
0.001111111112 + -0.06666666667x + x2 = 0.000311111112

Factor a perfect square on the left side:
(x + -0.03333333334)(x + -0.03333333334) = 0.000311111112

Calculate the square root of the right side: 0.017638342

Break this problem into two subproblems by setting 
(x + -0.03333333334) equal to 0.017638342 and -0.017638342.


Subproblem 1
x + -0.03333333334 = 0.017638342

Simplifying
x + -0.03333333334 = 0.017638342

Reorder the terms:
-0.03333333334 + x = 0.017638342

Solving
-0.03333333334 + x = 0.017638342

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 = 0.017638342 + 0.03333333334

Combine like terms: -0.03333333334 + 0.03333333334 = 0.00000000000
0.00000000000 + x = 0.017638342 + 0.03333333334
x = 0.017638342 + 0.03333333334

Combine like terms: 0.017638342 + 0.03333333334 = 0.05097167534
x = 0.05097167534

Simplifying
x = 0.05097167534


Subproblem 2
x + -0.03333333334 = -0.017638342

Simplifying
x + -0.03333333334 = -0.017638342

Reorder the terms:
-0.03333333334 + x = -0.017638342

Solving
-0.03333333334 + x = -0.017638342

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 = -0.017638342 + 0.03333333334

Combine like terms: -0.03333333334 + 0.03333333334 = 0.00000000000
0.00000000000 + x = -0.017638342 + 0.03333333334
x = -0.017638342 + 0.03333333334

Combine like terms: -0.017638342 + 0.03333333334 = 0.01569499134
x = 0.01569499134

Simplifying
x = 0.01569499134


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.05097167534, 0.01569499134}

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