0.5x^2-6x+17.5=0

Solution for 0.5x^2-6x+17.5=0 equation:

Simplifying
0.5x2 + -6x + 17.5 = 0

Reorder the terms:
17.5 + -6x + 0.5x2 = 0

Solving
17.5 + -6x + 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'.
35 + -12x + x2 = 0

Move the constant term to the right:

Add '-35' to each side of the equation.
35 + -12x + -35 + x2 = 0 + -35

Reorder the terms:
35 + -35 + -12x + x2 = 0 + -35

Combine like terms: 35 + -35 = 0
0 + -12x + x2 = 0 + -35
-12x + x2 = 0 + -35

Combine like terms: 0 + -35 = -35
-12x + x2 = -35

The x term is -12x.  Take half its coefficient (-6).
Square it (36) and add it to both sides.

Add '36' to each side of the equation.
-12x + 36 + x2 = -35 + 36

Reorder the terms:
36 + -12x + x2 = -35 + 36

Combine like terms: -35 + 36 = 1
36 + -12x + x2 = 1

Factor a perfect square on the left side:
(x + -6)(x + -6) = 1

Calculate the square root of the right side: 1

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

Subproblem 1
x + -6 = 1

Simplifying
x + -6 = 1

Reorder the terms:
-6 + x = 1

Solving
-6 + x = 1

Solving for variable 'x'.

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

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

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

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

Simplifying
x = 7

Subproblem 2
x + -6 = -1

Simplifying
x + -6 = -1

Reorder the terms:
-6 + x = -1

Solving
-6 + x = -1

Solving for variable 'x'.

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

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

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

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

Simplifying
x = 5

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