2z^2+6z+7=0

Solution for 2z^2+6z+7=0 equation:

Simplifying
2z2 + 6z + 7 = 0

Reorder the terms:
7 + 6z + 2z2 = 0

Solving
7 + 6z + 2z2 = 0

Solving for variable 'z'.

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

Divide each side by '2'.
3.5 + 3z + z2 = 0

Move the constant term to the right:

Add '-3.5' to each side of the equation.
3.5 + 3z + -3.5 + z2 = 0 + -3.5

Reorder the terms:
3.5 + -3.5 + 3z + z2 = 0 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + 3z + z2 = 0 + -3.5
3z + z2 = 0 + -3.5

Combine like terms: 0 + -3.5 = -3.5
3z + z2 = -3.5

The z term is 3z.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3z + 2.25 + z2 = -3.5 + 2.25

Reorder the terms:
2.25 + 3z + z2 = -3.5 + 2.25

Combine like terms: -3.5 + 2.25 = -1.25
2.25 + 3z + z2 = -1.25

Factor a perfect square on the left side:
(z + 1.5)(z + 1.5) = -1.25

Can't calculate square root of the right side.

The solution to this equation could not be determined.