z^2-5z+21=0

Solution for z^2-5z+21=0 equation:

Simplifying
z2 + -5z + 21 = 0

Reorder the terms:
21 + -5z + z2 = 0

Solving
21 + -5z + z2 = 0

Solving for variable 'z'.

Begin completing the square.

Move the constant term to the right:

Add '-21' to each side of the equation.
21 + -5z + -21 + z2 = 0 + -21

Reorder the terms:
21 + -21 + -5z + z2 = 0 + -21

Combine like terms: 21 + -21 = 0
0 + -5z + z2 = 0 + -21
-5z + z2 = 0 + -21

Combine like terms: 0 + -21 = -21
-5z + z2 = -21

The z term is -5z.  Take half its coefficient (-2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
-5z + 6.25 + z2 = -21 + 6.25

Reorder the terms:
6.25 + -5z + z2 = -21 + 6.25

Combine like terms: -21 + 6.25 = -14.75
6.25 + -5z + z2 = -14.75

Factor a perfect square on the left side:
(z + -2.5)(z + -2.5) = -14.75

Can't calculate square root of the right side.

The solution to this equation could not be determined.