4z^2-12z+13=0

Solution for 4z^2-12z+13=0 equation:

Simplifying
4z2 + -12z + 13 = 0

Reorder the terms:
13 + -12z + 4z2 = 0

Solving
13 + -12z + 4z2 = 0

Solving for variable 'z'.

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

Divide each side by '4'.
3.25 + -3z + z2 = 0

Move the constant term to the right:

Add '-3.25' to each side of the equation.
3.25 + -3z + -3.25 + z2 = 0 + -3.25

Reorder the terms:
3.25 + -3.25 + -3z + z2 = 0 + -3.25

Combine like terms: 3.25 + -3.25 = 0.00
0.00 + -3z + z2 = 0 + -3.25
-3z + z2 = 0 + -3.25

Combine like terms: 0 + -3.25 = -3.25
-3z + z2 = -3.25

The z term is -3z.  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.
-3z + 2.25 + z2 = -3.25 + 2.25

Reorder the terms:
2.25 + -3z + z2 = -3.25 + 2.25

Combine like terms: -3.25 + 2.25 = -1
2.25 + -3z + z2 = -1

Factor a perfect square on the left side:
(z + -1.5)(z + -1.5) = -1

Can't calculate square root of the right side.

The solution to this equation could not be determined.