2z(z)+z=-50

Solution for 2z(z)+z=-50 equation:

Simplifying
2z(z) + z = -50

Multiply z * z
2z2 + z = -50

Reorder the terms:
z + 2z2 = -50

Solving
z + 2z2 = -50

Solving for variable 'z'.

Reorder the terms:
50 + z + 2z2 = -50 + 50

Combine like terms: -50 + 50 = 0
50 + z + 2z2 = 0

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

Divide each side by '2'.
25 + 0.5z + z2 = 0

Move the constant term to the right:

Add '-25' to each side of the equation.
25 + 0.5z + -25 + z2 = 0 + -25

Reorder the terms:
25 + -25 + 0.5z + z2 = 0 + -25

Combine like terms: 25 + -25 = 0
0 + 0.5z + z2 = 0 + -25
0.5z + z2 = 0 + -25

Combine like terms: 0 + -25 = -25
0.5z + z2 = -25

The z term is z.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
0.5z + 0.25 + z2 = -25 + 0.25

Reorder the terms:
0.25 + 0.5z + z2 = -25 + 0.25

Combine like terms: -25 + 0.25 = -24.75
0.25 + 0.5z + z2 = -24.75

Factor a perfect square on the left side:
(z + 0.5)(z + 0.5) = -24.75

Can't calculate square root of the right side.

The solution to this equation could not be determined.