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

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

Simplifying
0.1x2 + -0.3x + -1 = 0

Reorder the terms:
-1 + -0.3x + 0.1x2 = 0

Solving
-1 + -0.3x + 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'.
-10 + -3x + x2 = 0

Move the constant term to the right:

Add '10' to each side of the equation.
-10 + -3x + 10 + x2 = 0 + 10

Reorder the terms:
-10 + 10 + -3x + x2 = 0 + 10

Combine like terms: -10 + 10 = 0
0 + -3x + x2 = 0 + 10
-3x + x2 = 0 + 10

Combine like terms: 0 + 10 = 10
-3x + x2 = 10

The x term is -3x.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3x + 2.25 + x2 = 10 + 2.25

Reorder the terms:
2.25 + -3x + x2 = 10 + 2.25

Combine like terms: 10 + 2.25 = 12.25
2.25 + -3x + x2 = 12.25

Factor a perfect square on the left side:
(x + -1.5)(x + -1.5) = 12.25

Calculate the square root of the right side: 3.5

Break this problem into two subproblems by setting 
(x + -1.5) equal to 3.5 and -3.5.

Subproblem 1
x + -1.5 = 3.5

Simplifying
x + -1.5 = 3.5

Reorder the terms:
-1.5 + x = 3.5

Solving
-1.5 + x = 3.5

Solving for variable 'x'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + x = 3.5 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + x = 3.5 + 1.5
x = 3.5 + 1.5

Combine like terms: 3.5 + 1.5 = 5
x = 5

Simplifying
x = 5

Subproblem 2
x + -1.5 = -3.5

Simplifying
x + -1.5 = -3.5

Reorder the terms:
-1.5 + x = -3.5

Solving
-1.5 + x = -3.5

Solving for variable 'x'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + x = -3.5 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + x = -3.5 + 1.5
x = -3.5 + 1.5

Combine like terms: -3.5 + 1.5 = -2
x = -2

Simplifying
x = -2

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5, -2}