0.006x^2+0.2x=50

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Solution for 0.006x^2+0.2x=50 equation: 


Simplifying
0.006x2 + 0.2x = 50

Reorder the terms:
0.2x + 0.006x2 = 50

Solving
0.2x + 0.006x2 = 50

Solving for variable 'x'.

Reorder the terms:
-50 + 0.2x + 0.006x2 = 50 + -50

Combine like terms: 50 + -50 = 0
-50 + 0.2x + 0.006x2 = 0

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

Divide each side by '0.006'.
-8333.333333 + 33.33333333x + x2 = 0

Move the constant term to the right:

Add '8333.333333' to each side of the equation.
-8333.333333 + 33.33333333x + 8333.333333 + x2 = 0 + 8333.333333

Reorder the terms:
-8333.333333 + 8333.333333 + 33.33333333x + x2 = 0 + 8333.333333

Combine like terms: -8333.333333 + 8333.333333 = 0.000000
0.000000 + 33.33333333x + x2 = 0 + 8333.333333
33.33333333x + x2 = 0 + 8333.333333

Combine like terms: 0 + 8333.333333 = 8333.333333
33.33333333x + x2 = 8333.333333

The x term is 33.33333333x.  Take half its coefficient (16.66666667).
Square it (277.7777779) and add it to both sides.

Add '277.7777779' to each side of the equation.
33.33333333x + 277.7777779 + x2 = 8333.333333 + 277.7777779

Reorder the terms:
277.7777779 + 33.33333333x + x2 = 8333.333333 + 277.7777779

Combine like terms: 8333.333333 + 277.7777779 = 8611.1111109
277.7777779 + 33.33333333x + x2 = 8611.1111109

Factor a perfect square on the left side:
(x + 16.66666667)(x + 16.66666667) = 8611.1111109

Calculate the square root of the right side: 92.796072713

Break this problem into two subproblems by setting 
(x + 16.66666667) equal to 92.796072713 and -92.796072713.


Subproblem 1
x + 16.66666667 = 92.796072713

Simplifying
x + 16.66666667 = 92.796072713

Reorder the terms:
16.66666667 + x = 92.796072713

Solving
16.66666667 + x = 92.796072713

Solving for variable 'x'.

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

Add '-16.66666667' to each side of the equation.
16.66666667 + -16.66666667 + x = 92.796072713 + -16.66666667

Combine like terms: 16.66666667 + -16.66666667 = 0.00000000
0.00000000 + x = 92.796072713 + -16.66666667
x = 92.796072713 + -16.66666667

Combine like terms: 92.796072713 + -16.66666667 = 76.129406043
x = 76.129406043

Simplifying
x = 76.129406043


Subproblem 2
x + 16.66666667 = -92.796072713

Simplifying
x + 16.66666667 = -92.796072713

Reorder the terms:
16.66666667 + x = -92.796072713

Solving
16.66666667 + x = -92.796072713

Solving for variable 'x'.

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

Add '-16.66666667' to each side of the equation.
16.66666667 + -16.66666667 + x = -92.796072713 + -16.66666667

Combine like terms: 16.66666667 + -16.66666667 = 0.00000000
0.00000000 + x = -92.796072713 + -16.66666667
x = -92.796072713 + -16.66666667

Combine like terms: -92.796072713 + -16.66666667 = -109.462739383
x = -109.462739383

Simplifying
x = -109.462739383


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {76.129406043, -109.462739383}

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