2a^2-2a+6=0

Solution for 2a^2-2a+6=0 equation:

Simplifying
2a2 + -2a + 6 = 0

Reorder the terms:
6 + -2a + 2a2 = 0

Solving
6 + -2a + 2a2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '2'.
2(3 + -1a + a2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(3 + -1a + a2)' equal to zero and attempt to solve:

Simplifying
3 + -1a + a2 = 0

Solving
3 + -1a + a2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-3' to each side of the equation.
3 + -1a + -3 + a2 = 0 + -3

Reorder the terms:
3 + -3 + -1a + a2 = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1a + a2 = 0 + -3
-1a + a2 = 0 + -3

Combine like terms: 0 + -3 = -3
-1a + a2 = -3

The a term is -1a.  Take half its coefficient (-0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-1a + 0.25 + a2 = -3 + 0.25

Reorder the terms:
0.25 + -1a + a2 = -3 + 0.25

Combine like terms: -3 + 0.25 = -2.75
0.25 + -1a + a2 = -2.75

Factor a perfect square on the left side:
(a + -0.5)(a + -0.5) = -2.75

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.