a^2-2a+0.5=0

Solution for a^2-2a+0.5=0 equation:

Simplifying
a2 + -2a + 0.5 = 0

Reorder the terms:
0.5 + -2a + a2 = 0

Solving
0.5 + -2a + a2 = 0

Solving for variable 'a'.

Begin completing the square.

Move the constant term to the right:

Add '-0.5' to each side of the equation.
0.5 + -2a + -0.5 + a2 = 0 + -0.5

Reorder the terms:
0.5 + -0.5 + -2a + a2 = 0 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + -2a + a2 = 0 + -0.5
-2a + a2 = 0 + -0.5

Combine like terms: 0 + -0.5 = -0.5
-2a + a2 = -0.5

The a term is -2a.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2a + 1 + a2 = -0.5 + 1

Reorder the terms:
1 + -2a + a2 = -0.5 + 1

Combine like terms: -0.5 + 1 = 0.5
1 + -2a + a2 = 0.5

Factor a perfect square on the left side:
(a + -1)(a + -1) = 0.5

Calculate the square root of the right side: 0.707106781

Break this problem into two subproblems by setting 
(a + -1) equal to 0.707106781 and -0.707106781.

Subproblem 1
a + -1 = 0.707106781

Simplifying
a + -1 = 0.707106781

Reorder the terms:
-1 + a = 0.707106781

Solving
-1 + a = 0.707106781

Solving for variable 'a'.

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

Add '1' to each side of the equation.
-1 + 1 + a = 0.707106781 + 1

Combine like terms: -1 + 1 = 0
0 + a = 0.707106781 + 1
a = 0.707106781 + 1

Combine like terms: 0.707106781 + 1 = 1.707106781
a = 1.707106781

Simplifying
a = 1.707106781

Subproblem 2
a + -1 = -0.707106781

Simplifying
a + -1 = -0.707106781

Reorder the terms:
-1 + a = -0.707106781

Solving
-1 + a = -0.707106781

Solving for variable 'a'.

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

Add '1' to each side of the equation.
-1 + 1 + a = -0.707106781 + 1

Combine like terms: -1 + 1 = 0
0 + a = -0.707106781 + 1
a = -0.707106781 + 1

Combine like terms: -0.707106781 + 1 = 0.292893219
a = 0.292893219

Simplifying
a = 0.292893219

Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {1.707106781, 0.292893219}