0.1x^2-0.2x-3.5=0

Solution for 0.1x^2-0.2x-3.5=0 equation:

Simplifying
0.1x2 + -0.2x + -3.5 = 0

Reorder the terms:
-3.5 + -0.2x + 0.1x2 = 0

Solving
-3.5 + -0.2x + 0.1x2 = 0

Solving for variable 'x'.

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

Divide each side by '0.1'.
-35 + -2x + x2 = 0

Move the constant term to the right:

Add '35' to each side of the equation.
-35 + -2x + 35 + x2 = 0 + 35

Reorder the terms:
-35 + 35 + -2x + x2 = 0 + 35

Combine like terms: -35 + 35 = 0
0 + -2x + x2 = 0 + 35
-2x + x2 = 0 + 35

Combine like terms: 0 + 35 = 35
-2x + x2 = 35

The x term is -2x.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2x + 1 + x2 = 35 + 1

Reorder the terms:
1 + -2x + x2 = 35 + 1

Combine like terms: 35 + 1 = 36
1 + -2x + x2 = 36

Factor a perfect square on the left side:
(x + -1)(x + -1) = 36

Calculate the square root of the right side: 6

Break this problem into two subproblems by setting 
(x + -1) equal to 6 and -6.

Subproblem 1
x + -1 = 6

Simplifying
x + -1 = 6

Reorder the terms:
-1 + x = 6

Solving
-1 + x = 6

Solving for variable 'x'.

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

Add '1' to each side of the equation.
-1 + 1 + x = 6 + 1

Combine like terms: -1 + 1 = 0
0 + x = 6 + 1
x = 6 + 1

Combine like terms: 6 + 1 = 7
x = 7

Simplifying
x = 7

Subproblem 2
x + -1 = -6

Simplifying
x + -1 = -6

Reorder the terms:
-1 + x = -6

Solving
-1 + x = -6

Solving for variable 'x'.

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

Add '1' to each side of the equation.
-1 + 1 + x = -6 + 1

Combine like terms: -1 + 1 = 0
0 + x = -6 + 1
x = -6 + 1

Combine like terms: -6 + 1 = -5
x = -5

Simplifying
x = -5

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {7, -5}