-.1x^2+.1x+3=0

Solution for -.1x^2+.1x+3=0 equation:

Simplifying
-0.1x2 + 0.1x + 3 = 0

Reorder the terms:
3 + 0.1x + -0.1x2 = 0

Solving
3 + 0.1x + -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'.
-30 + -1x + x2 = 0

Move the constant term to the right:

Add '30' to each side of the equation.
-30 + -1x + 30 + x2 = 0 + 30

Reorder the terms:
-30 + 30 + -1x + x2 = 0 + 30

Combine like terms: -30 + 30 = 0
0 + -1x + x2 = 0 + 30
-1x + x2 = 0 + 30

Combine like terms: 0 + 30 = 30
-1x + x2 = 30

The x term is -1x.  Take half its coefficient (-0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-1x + 0.25 + x2 = 30 + 0.25

Reorder the terms:
0.25 + -1x + x2 = 30 + 0.25

Combine like terms: 30 + 0.25 = 30.25
0.25 + -1x + x2 = 30.25

Factor a perfect square on the left side:
(x + -0.5)(x + -0.5) = 30.25

Calculate the square root of the right side: 5.5

Break this problem into two subproblems by setting 
(x + -0.5) equal to 5.5 and -5.5.

Subproblem 1
x + -0.5 = 5.5

Simplifying
x + -0.5 = 5.5

Reorder the terms:
-0.5 + x = 5.5

Solving
-0.5 + x = 5.5

Solving for variable 'x'.

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

Add '0.5' to each side of the equation.
-0.5 + 0.5 + x = 5.5 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + x = 5.5 + 0.5
x = 5.5 + 0.5

Combine like terms: 5.5 + 0.5 = 6
x = 6

Simplifying
x = 6

Subproblem 2
x + -0.5 = -5.5

Simplifying
x + -0.5 = -5.5

Reorder the terms:
-0.5 + x = -5.5

Solving
-0.5 + x = -5.5

Solving for variable 'x'.

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

Add '0.5' to each side of the equation.
-0.5 + 0.5 + x = -5.5 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + x = -5.5 + 0.5
x = -5.5 + 0.5

Combine like terms: -5.5 + 0.5 = -5
x = -5

Simplifying
x = -5

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6, -5}