.5x^2-x-1.5=0

Solution for .5x^2-x-1.5=0 equation:

Simplifying
0.5x2 + -1x + -1.5 = 0

Reorder the terms:
-1.5 + -1x + 0.5x2 = 0

Solving
-1.5 + -1x + 0.5x2 = 0

Solving for variable 'x'.

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

Divide each side by '0.5'.
-3 + -2x + x2 = 0

Move the constant term to the right:

Add '3' to each side of the equation.
-3 + -2x + 3 + x2 = 0 + 3

Reorder the terms:
-3 + 3 + -2x + x2 = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -2x + x2 = 0 + 3
-2x + x2 = 0 + 3

Combine like terms: 0 + 3 = 3
-2x + x2 = 3

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 = 3 + 1

Reorder the terms:
1 + -2x + x2 = 3 + 1

Combine like terms: 3 + 1 = 4
1 + -2x + x2 = 4

Factor a perfect square on the left side:
(x + -1)(x + -1) = 4

Calculate the square root of the right side: 2

Break this problem into two subproblems by setting 
(x + -1) equal to 2 and -2.

Subproblem 1
x + -1 = 2

Simplifying
x + -1 = 2

Reorder the terms:
-1 + x = 2

Solving
-1 + x = 2

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 = 2 + 1

Combine like terms: -1 + 1 = 0
0 + x = 2 + 1
x = 2 + 1

Combine like terms: 2 + 1 = 3
x = 3

Simplifying
x = 3

Subproblem 2
x + -1 = -2

Simplifying
x + -1 = -2

Reorder the terms:
-1 + x = -2

Solving
-1 + x = -2

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 = -2 + 1

Combine like terms: -1 + 1 = 0
0 + x = -2 + 1
x = -2 + 1

Combine like terms: -2 + 1 = -1
x = -1

Simplifying
x = -1

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3, -1}