41+8z=-z^2

Solution for 41+8z=-z^2 equation:

Simplifying
41 + 8z = -1z2

Solving
41 + 8z = -1z2

Solving for variable 'z'.

Combine like terms: -1z2 + z2 = 0
41 + 8z + z2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-41' to each side of the equation.
41 + 8z + -41 + z2 = 0 + -41

Reorder the terms:
41 + -41 + 8z + z2 = 0 + -41

Combine like terms: 41 + -41 = 0
0 + 8z + z2 = 0 + -41
8z + z2 = 0 + -41

Combine like terms: 0 + -41 = -41
8z + z2 = -41

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 = -41 + 16

Reorder the terms:
16 + 8z + z2 = -41 + 16

Combine like terms: -41 + 16 = -25
16 + 8z + z2 = -25

Factor a perfect square on the left side:
(z + 4)(z + 4) = -25

Can't calculate square root of the right side.

The solution to this equation could not be determined.