2a^2-6a+13=0

Solution for 2a^2-6a+13=0 equation:

Simplifying
2a2 + -6a + 13 = 0

Reorder the terms:
13 + -6a + 2a2 = 0

Solving
13 + -6a + 2a2 = 0

Solving for variable 'a'.

Begin completing the square.  Divide all terms by
2 the coefficient of the squared term: 

Divide each side by '2'.
6.5 + -3a + a2 = 0

Move the constant term to the right:

Add '-6.5' to each side of the equation.
6.5 + -3a + -6.5 + a2 = 0 + -6.5

Reorder the terms:
6.5 + -6.5 + -3a + a2 = 0 + -6.5

Combine like terms: 6.5 + -6.5 = 0.0
0.0 + -3a + a2 = 0 + -6.5
-3a + a2 = 0 + -6.5

Combine like terms: 0 + -6.5 = -6.5
-3a + a2 = -6.5

The a term is -3a.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3a + 2.25 + a2 = -6.5 + 2.25

Reorder the terms:
2.25 + -3a + a2 = -6.5 + 2.25

Combine like terms: -6.5 + 2.25 = -4.25
2.25 + -3a + a2 = -4.25

Factor a perfect square on the left side:
(a + -1.5)(a + -1.5) = -4.25

Can't calculate square root of the right side.

The solution to this equation could not be determined.