-.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 = 1
x = 1

Simplifying
x = 1

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 = -3
x = -3

Simplifying
x = -3

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