z^2-8z+19=0

Solution for z^2-8z+19=0 equation:

Simplifying
z2 + -8z + 19 = 0

Reorder the terms:
19 + -8z + z2 = 0

Solving
19 + -8z + z2 = 0

Solving for variable 'z'.

Begin completing the square.

Move the constant term to the right:

Add '-19' to each side of the equation.
19 + -8z + -19 + z2 = 0 + -19

Reorder the terms:
19 + -19 + -8z + z2 = 0 + -19

Combine like terms: 19 + -19 = 0
0 + -8z + z2 = 0 + -19
-8z + z2 = 0 + -19

Combine like terms: 0 + -19 = -19
-8z + z2 = -19

The z term is -8z.  Take half its coefficient (-4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
-8z + 16 + z2 = -19 + 16

Reorder the terms:
16 + -8z + z2 = -19 + 16

Combine like terms: -19 + 16 = -3
16 + -8z + z2 = -3

Factor a perfect square on the left side:
(z + -4)(z + -4) = -3

Can't calculate square root of the right side.

The solution to this equation could not be determined.