z^2+6z+10=0

Solution for z^2+6z+10=0 equation:

Simplifying
z2 + 6z + 10 = 0

Reorder the terms:
10 + 6z + z2 = 0

Solving
10 + 6z + 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 + 6z + -10 + z2 = 0 + -10

Reorder the terms:
10 + -10 + 6z + z2 = 0 + -10

Combine like terms: 10 + -10 = 0
0 + 6z + z2 = 0 + -10
6z + z2 = 0 + -10

Combine like terms: 0 + -10 = -10
6z + z2 = -10

The z term is 6z.  Take half its coefficient (3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
6z + 9 + z2 = -10 + 9

Reorder the terms:
9 + 6z + z2 = -10 + 9

Combine like terms: -10 + 9 = -1
9 + 6z + z2 = -1

Factor a perfect square on the left side:
(z + 3)(z + 3) = -1

Can't calculate square root of the right side.

The solution to this equation could not be determined.