z^2+4z=-8

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Solution for z^2+4z=-8 equation:


Simplifying
z2 + 4z = -8

Reorder the terms:
4z + z2 = -8

Solving
4z + z2 = -8

Solving for variable 'z'.

Reorder the terms:
8 + 4z + z2 = -8 + 8

Combine like terms: -8 + 8 = 0
8 + 4z + z2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-8' to each side of the equation.
8 + 4z + -8 + z2 = 0 + -8

Reorder the terms:
8 + -8 + 4z + z2 = 0 + -8

Combine like terms: 8 + -8 = 0
0 + 4z + z2 = 0 + -8
4z + z2 = 0 + -8

Combine like terms: 0 + -8 = -8
4z + z2 = -8

The z term is 4z.  Take half its coefficient (2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
4z + 4 + z2 = -8 + 4

Reorder the terms:
4 + 4z + z2 = -8 + 4

Combine like terms: -8 + 4 = -4
4 + 4z + z2 = -4

Factor a perfect square on the left side:
(z + 2)(z + 2) = -4

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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