5z^2+2z+10=0

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

Simplifying
5z2 + 2z + 10 = 0

Reorder the terms:
10 + 2z + 5z2 = 0

Solving
10 + 2z + 5z2 = 0

Solving for variable 'z'.

Begin completing the square.  Divide all terms by
5 the coefficient of the squared term: 

Divide each side by '5'.
2 + 0.4z + z2 = 0

Move the constant term to the right:

Add '-2' to each side of the equation.
2 + 0.4z + -2 + z2 = 0 + -2

Reorder the terms:
2 + -2 + 0.4z + z2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 0.4z + z2 = 0 + -2
0.4z + z2 = 0 + -2

Combine like terms: 0 + -2 = -2
0.4z + z2 = -2

The z term is 0.4z.  Take half its coefficient (0.2).
Square it (0.04) and add it to both sides.

Add '0.04' to each side of the equation.
0.4z + 0.04 + z2 = -2 + 0.04

Reorder the terms:
0.04 + 0.4z + z2 = -2 + 0.04

Combine like terms: -2 + 0.04 = -1.96
0.04 + 0.4z + z2 = -1.96

Factor a perfect square on the left side:
(z + 0.2)(z + 0.2) = -1.96

Can't calculate square root of the right side.

The solution to this equation could not be determined.