2a^2-2a+12=0

Solution for 2a^2-2a+12=0 equation:

Simplifying
2a2 + -2a + 12 = 0

Reorder the terms:
12 + -2a + 2a2 = 0

Solving
12 + -2a + 2a2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '2'.
2(6 + -1a + a2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(6 + -1a + a2)' equal to zero and attempt to solve:

Simplifying
6 + -1a + a2 = 0

Solving
6 + -1a + a2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-6' to each side of the equation.
6 + -1a + -6 + a2 = 0 + -6

Reorder the terms:
6 + -6 + -1a + a2 = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1a + a2 = 0 + -6
-1a + a2 = 0 + -6

Combine like terms: 0 + -6 = -6
-1a + a2 = -6

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 = -6 + 0.25

Reorder the terms:
0.25 + -1a + a2 = -6 + 0.25

Combine like terms: -6 + 0.25 = -5.75
0.25 + -1a + a2 = -5.75

Factor a perfect square on the left side:
(a + -0.5)(a + -0.5) = -5.75

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.