0.03x^2-0.5x+0.06=0

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Solution for 0.03x^2-0.5x+0.06=0 equation: 


Simplifying
0.03x2 + -0.5x + 0.06 = 0

Reorder the terms:
0.06 + -0.5x + 0.03x2 = 0

Solving
0.06 + -0.5x + 0.03x2 = 0

Solving for variable 'x'.

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

Divide each side by '0.03'.
2 + -16.66666667x + x2 = 0

Move the constant term to the right:

Add '-2' to each side of the equation.
2 + -16.66666667x + -2 + x2 = 0 + -2

Reorder the terms:
2 + -2 + -16.66666667x + x2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -16.66666667x + x2 = 0 + -2
-16.66666667x + x2 = 0 + -2

Combine like terms: 0 + -2 = -2
-16.66666667x + x2 = -2

The x term is -16.66666667x.  Take half its coefficient (-8.333333335).
Square it (69.44444447) and add it to both sides.

Add '69.44444447' to each side of the equation.
-16.66666667x + 69.44444447 + x2 = -2 + 69.44444447

Reorder the terms:
69.44444447 + -16.66666667x + x2 = -2 + 69.44444447

Combine like terms: -2 + 69.44444447 = 67.44444447
69.44444447 + -16.66666667x + x2 = 67.44444447

Factor a perfect square on the left side:
(x + -8.333333335)(x + -8.333333335) = 67.44444447

Calculate the square root of the right side: 8.212456665

Break this problem into two subproblems by setting 
(x + -8.333333335) equal to 8.212456665 and -8.212456665.


Subproblem 1
x + -8.333333335 = 8.212456665

Simplifying
x + -8.333333335 = 8.212456665

Reorder the terms:
-8.333333335 + x = 8.212456665

Solving
-8.333333335 + x = 8.212456665

Solving for variable 'x'.

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

Add '8.333333335' to each side of the equation.
-8.333333335 + 8.333333335 + x = 8.212456665 + 8.333333335

Combine like terms: -8.333333335 + 8.333333335 = 0.000000000
0.000000000 + x = 8.212456665 + 8.333333335
x = 8.212456665 + 8.333333335

Combine like terms: 8.212456665 + 8.333333335 = 16.54579
x = 16.54579

Simplifying
x = 16.54579


Subproblem 2
x + -8.333333335 = -8.212456665

Simplifying
x + -8.333333335 = -8.212456665

Reorder the terms:
-8.333333335 + x = -8.212456665

Solving
-8.333333335 + x = -8.212456665

Solving for variable 'x'.

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

Add '8.333333335' to each side of the equation.
-8.333333335 + 8.333333335 + x = -8.212456665 + 8.333333335

Combine like terms: -8.333333335 + 8.333333335 = 0.000000000
0.000000000 + x = -8.212456665 + 8.333333335
x = -8.212456665 + 8.333333335

Combine like terms: -8.212456665 + 8.333333335 = 0.12087667
x = 0.12087667

Simplifying
x = 0.12087667


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {16.54579, 0.12087667}

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