.02x^2+4.1x-30=0

Solution for .02x^2+4.1x-30=0 equation:

Simplifying
0.02x2 + 4.1x + -30 = 0

Reorder the terms:
-30 + 4.1x + 0.02x2 = 0

Solving
-30 + 4.1x + 0.02x2 = 0

Solving for variable 'x'.

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

Divide each side by '0.02'.
-1500 + 205x + x2 = 0

Move the constant term to the right:

Add '1500' to each side of the equation.
-1500 + 205x + 1500 + x2 = 0 + 1500

Reorder the terms:
-1500 + 1500 + 205x + x2 = 0 + 1500

Combine like terms: -1500 + 1500 = 0
0 + 205x + x2 = 0 + 1500
205x + x2 = 0 + 1500

Combine like terms: 0 + 1500 = 1500
205x + x2 = 1500

The x term is 205x.  Take half its coefficient (102.5).
Square it (10506.25) and add it to both sides.

Add '10506.25' to each side of the equation.
205x + 10506.25 + x2 = 1500 + 10506.25

Reorder the terms:
10506.25 + 205x + x2 = 1500 + 10506.25

Combine like terms: 1500 + 10506.25 = 12006.25
10506.25 + 205x + x2 = 12006.25

Factor a perfect square on the left side:
(x + 102.5)(x + 102.5) = 12006.25

Calculate the square root of the right side: 109.573035004

Break this problem into two subproblems by setting 
(x + 102.5) equal to 109.573035004 and -109.573035004.

Subproblem 1
x + 102.5 = 109.573035004

Simplifying
x + 102.5 = 109.573035004

Reorder the terms:
102.5 + x = 109.573035004

Solving
102.5 + x = 109.573035004

Solving for variable 'x'.

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

Add '-102.5' to each side of the equation.
102.5 + -102.5 + x = 109.573035004 + -102.5

Combine like terms: 102.5 + -102.5 = 0.0
0.0 + x = 109.573035004 + -102.5
x = 109.573035004 + -102.5

Combine like terms: 109.573035004 + -102.5 = 7.073035004
x = 7.073035004

Simplifying
x = 7.073035004

Subproblem 2
x + 102.5 = -109.573035004

Simplifying
x + 102.5 = -109.573035004

Reorder the terms:
102.5 + x = -109.573035004

Solving
102.5 + x = -109.573035004

Solving for variable 'x'.

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

Add '-102.5' to each side of the equation.
102.5 + -102.5 + x = -109.573035004 + -102.5

Combine like terms: 102.5 + -102.5 = 0.0
0.0 + x = -109.573035004 + -102.5
x = -109.573035004 + -102.5

Combine like terms: -109.573035004 + -102.5 = -212.073035004
x = -212.073035004

Simplifying
x = -212.073035004

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {7.073035004, -212.073035004}