z^2+5z+10=0

Solution for z^2+5z+10=0 equation:

Simplifying
z2 + 5z + 10 = 0

Reorder the terms:
10 + 5z + z2 = 0

Solving
10 + 5z + z2 = 0

Solving for variable 'z'.

Begin completing the square.

Move the constant term to the right:

Add '-10' to each side of the equation.
10 + 5z + -10 + z2 = 0 + -10

Reorder the terms:
10 + -10 + 5z + z2 = 0 + -10

Combine like terms: 10 + -10 = 0
0 + 5z + z2 = 0 + -10
5z + z2 = 0 + -10

Combine like terms: 0 + -10 = -10
5z + z2 = -10

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 = -10 + 6.25

Reorder the terms:
6.25 + 5z + z2 = -10 + 6.25

Combine like terms: -10 + 6.25 = -3.75
6.25 + 5z + z2 = -3.75

Factor a perfect square on the left side:
(z + 2.5)(z + 2.5) = -3.75

Can't calculate square root of the right side.

The solution to this equation could not be determined.