z^2+7z=-42.50

Solution for z^2+7z=-42.50 equation:

Simplifying
z2 + 7z = -42.50

Reorder the terms:
7z + z2 = -42.50

Solving
7z + z2 = -42.50

Solving for variable 'z'.

Reorder the terms:
42.50 + 7z + z2 = -42.50 + 42.50

Combine like terms: -42.50 + 42.50 = 0.00
42.50 + 7z + z2 = 0.00

Begin completing the square.

Move the constant term to the right:

Add '-42.50' to each side of the equation.
42.50 + 7z + -42.50 + z2 = 0.00 + -42.50

Reorder the terms:
42.50 + -42.50 + 7z + z2 = 0.00 + -42.50

Combine like terms: 42.50 + -42.50 = 0.00
0.00 + 7z + z2 = 0.00 + -42.50
7z + z2 = 0.00 + -42.50

Combine like terms: 0.00 + -42.50 = -42.5
7z + z2 = -42.5

The z term is 7z.  Take half its coefficient (3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
7z + 12.25 + z2 = -42.5 + 12.25

Reorder the terms:
12.25 + 7z + z2 = -42.5 + 12.25

Combine like terms: -42.5 + 12.25 = -30.25
12.25 + 7z + z2 = -30.25

Factor a perfect square on the left side:
(z + 3.5)(z + 3.5) = -30.25

Can't calculate square root of the right side.

The solution to this equation could not be determined.