4z^2-8z+29=0

Solution for 4z^2-8z+29=0 equation:

Simplifying
4z2 + -8z + 29 = 0

Reorder the terms:
29 + -8z + 4z2 = 0

Solving
29 + -8z + 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'.
7.25 + -2z + z2 = 0

Move the constant term to the right:

Add '-7.25' to each side of the equation.
7.25 + -2z + -7.25 + z2 = 0 + -7.25

Reorder the terms:
7.25 + -7.25 + -2z + z2 = 0 + -7.25

Combine like terms: 7.25 + -7.25 = 0.00
0.00 + -2z + z2 = 0 + -7.25
-2z + z2 = 0 + -7.25

Combine like terms: 0 + -7.25 = -7.25
-2z + z2 = -7.25

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

Add '1' to each side of the equation.
-2z + 1 + z2 = -7.25 + 1

Reorder the terms:
1 + -2z + z2 = -7.25 + 1

Combine like terms: -7.25 + 1 = -6.25
1 + -2z + z2 = -6.25

Factor a perfect square on the left side:
(z + -1)(z + -1) = -6.25

Can't calculate square root of the right side.

The solution to this equation could not be determined.