z^2-3z+40=0

Solution for z^2-3z+40=0 equation:

Simplifying
z2 + -3z + 40 = 0

Reorder the terms:
40 + -3z + z2 = 0

Solving
40 + -3z + z2 = 0

Solving for variable 'z'.

Begin completing the square.

Move the constant term to the right:

Add '-40' to each side of the equation.
40 + -3z + -40 + z2 = 0 + -40

Reorder the terms:
40 + -40 + -3z + z2 = 0 + -40

Combine like terms: 40 + -40 = 0
0 + -3z + z2 = 0 + -40
-3z + z2 = 0 + -40

Combine like terms: 0 + -40 = -40
-3z + z2 = -40

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 = -40 + 2.25

Reorder the terms:
2.25 + -3z + z2 = -40 + 2.25

Combine like terms: -40 + 2.25 = -37.75
2.25 + -3z + z2 = -37.75

Factor a perfect square on the left side:
(z + -1.5)(z + -1.5) = -37.75

Can't calculate square root of the right side.

The solution to this equation could not be determined.