z^2+5z=-15.25

Solution for z^2+5z=-15.25 equation:

Simplifying
z2 + 5z = -15.25

Reorder the terms:
5z + z2 = -15.25

Solving
5z + z2 = -15.25

Solving for variable 'z'.

Reorder the terms:
15.25 + 5z + z2 = -15.25 + 15.25

Combine like terms: -15.25 + 15.25 = 0.00
15.25 + 5z + z2 = 0.00

Begin completing the square.

Move the constant term to the right:

Add '-15.25' to each side of the equation.
15.25 + 5z + -15.25 + z2 = 0.00 + -15.25

Reorder the terms:
15.25 + -15.25 + 5z + z2 = 0.00 + -15.25

Combine like terms: 15.25 + -15.25 = 0.00
0.00 + 5z + z2 = 0.00 + -15.25
5z + z2 = 0.00 + -15.25

Combine like terms: 0.00 + -15.25 = -15.25
5z + z2 = -15.25

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 = -15.25 + 6.25

Reorder the terms:
6.25 + 5z + z2 = -15.25 + 6.25

Combine like terms: -15.25 + 6.25 = -9
6.25 + 5z + z2 = -9

Factor a perfect square on the left side:
(z + 2.5)(z + 2.5) = -9

Can't calculate square root of the right side.

The solution to this equation could not be determined.