4z^2+z+5=0

Solution for 4z^2+z+5=0 equation:

Simplifying
4z2 + z + 5 = 0

Reorder the terms:
5 + z + 4z2 = 0

Solving
5 + z + 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'.
1.25 + 0.25z + z2 = 0

Move the constant term to the right:

Add '-1.25' to each side of the equation.
1.25 + 0.25z + -1.25 + z2 = 0 + -1.25

Reorder the terms:
1.25 + -1.25 + 0.25z + z2 = 0 + -1.25

Combine like terms: 1.25 + -1.25 = 0.00
0.00 + 0.25z + z2 = 0 + -1.25
0.25z + z2 = 0 + -1.25

Combine like terms: 0 + -1.25 = -1.25
0.25z + z2 = -1.25

The z term is z.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
0.25z + 0.25 + z2 = -1.25 + 0.25

Reorder the terms:
0.25 + 0.25z + z2 = -1.25 + 0.25

Combine like terms: -1.25 + 0.25 = -1
0.25 + 0.25z + z2 = -1

Factor a perfect square on the left side:
(z + 0.5)(z + 0.5) = -1

Can't calculate square root of the right side.

The solution to this equation could not be determined.