z^2+5z+25=0

Solution for z^2+5z+25=0 equation:

Simplifying
z2 + 5z + 25 = 0

Reorder the terms:
25 + 5z + z2 = 0

Solving
25 + 5z + z2 = 0

Solving for variable 'z'.

Begin completing the square.

Move the constant term to the right:

Add '-25' to each side of the equation.
25 + 5z + -25 + z2 = 0 + -25

Reorder the terms:
25 + -25 + 5z + z2 = 0 + -25

Combine like terms: 25 + -25 = 0
0 + 5z + z2 = 0 + -25
5z + z2 = 0 + -25

Combine like terms: 0 + -25 = -25
5z + z2 = -25

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 = -25 + 6.25

Reorder the terms:
6.25 + 5z + z2 = -25 + 6.25

Combine like terms: -25 + 6.25 = -18.75
6.25 + 5z + z2 = -18.75

Factor a perfect square on the left side:
(z + 2.5)(z + 2.5) = -18.75

Can't calculate square root of the right side.

The solution to this equation could not be determined.