3x^2-2x+0.24=0

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Solution for 3x^2-2x+0.24=0 equation: 


Simplifying
3x2 + -2x + 0.24 = 0

Reorder the terms:
0.24 + -2x + 3x2 = 0

Solving
0.24 + -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'.
0.08 + -0.6666666667x + x2 = 0

Move the constant term to the right:

Add '-0.08' to each side of the equation.
0.08 + -0.6666666667x + -0.08 + x2 = 0 + -0.08

Reorder the terms:
0.08 + -0.08 + -0.6666666667x + x2 = 0 + -0.08

Combine like terms: 0.08 + -0.08 = 0.00
0.00 + -0.6666666667x + x2 = 0 + -0.08
-0.6666666667x + x2 = 0 + -0.08

Combine like terms: 0 + -0.08 = -0.08
-0.6666666667x + x2 = -0.08

The x term is -0.6666666667x.  Take half its coefficient (-0.3333333334).
Square it (0.1111111112) and add it to both sides.

Add '0.1111111112' to each side of the equation.
-0.6666666667x + 0.1111111112 + x2 = -0.08 + 0.1111111112

Reorder the terms:
0.1111111112 + -0.6666666667x + x2 = -0.08 + 0.1111111112

Combine like terms: -0.08 + 0.1111111112 = 0.0311111112
0.1111111112 + -0.6666666667x + x2 = 0.0311111112

Factor a perfect square on the left side:
(x + -0.3333333334)(x + -0.3333333334) = 0.0311111112

Calculate the square root of the right side: 0.176383421

Break this problem into two subproblems by setting 
(x + -0.3333333334) equal to 0.176383421 and -0.176383421.


Subproblem 1
x + -0.3333333334 = 0.176383421

Simplifying
x + -0.3333333334 = 0.176383421

Reorder the terms:
-0.3333333334 + x = 0.176383421

Solving
-0.3333333334 + x = 0.176383421

Solving for variable 'x'.

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

Add '0.3333333334' to each side of the equation.
-0.3333333334 + 0.3333333334 + x = 0.176383421 + 0.3333333334

Combine like terms: -0.3333333334 + 0.3333333334 = 0.0000000000
0.0000000000 + x = 0.176383421 + 0.3333333334
x = 0.176383421 + 0.3333333334

Combine like terms: 0.176383421 + 0.3333333334 = 0.5097167544
x = 0.5097167544

Simplifying
x = 0.5097167544


Subproblem 2
x + -0.3333333334 = -0.176383421

Simplifying
x + -0.3333333334 = -0.176383421

Reorder the terms:
-0.3333333334 + x = -0.176383421

Solving
-0.3333333334 + x = -0.176383421

Solving for variable 'x'.

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

Add '0.3333333334' to each side of the equation.
-0.3333333334 + 0.3333333334 + x = -0.176383421 + 0.3333333334

Combine like terms: -0.3333333334 + 0.3333333334 = 0.0000000000
0.0000000000 + x = -0.176383421 + 0.3333333334
x = -0.176383421 + 0.3333333334

Combine like terms: -0.176383421 + 0.3333333334 = 0.1569499124
x = 0.1569499124

Simplifying
x = 0.1569499124


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.5097167544, 0.1569499124}

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