4z^2+4z+1=-9

Solution for 4z^2+4z+1=-9 equation:

Simplifying
4z2 + 4z + 1 = -9

Reorder the terms:
1 + 4z + 4z2 = -9

Solving
1 + 4z + 4z2 = -9

Solving for variable 'z'.

Reorder the terms:
1 + 9 + 4z + 4z2 = -9 + 9

Combine like terms: 1 + 9 = 10
10 + 4z + 4z2 = -9 + 9

Combine like terms: -9 + 9 = 0
10 + 4z + 4z2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(5 + 2z + 2z2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(5 + 2z + 2z2)' equal to zero and attempt to solve:

Simplifying
5 + 2z + 2z2 = 0

Solving
5 + 2z + 2z2 = 0

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

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

Move the constant term to the right:

Add '-2.5' to each side of the equation.
2.5 + z + -2.5 + z2 = 0 + -2.5

Reorder the terms:
2.5 + -2.5 + z + z2 = 0 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + z + z2 = 0 + -2.5
z + z2 = 0 + -2.5

Combine like terms: 0 + -2.5 = -2.5
z + z2 = -2.5

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.
 + 0.25 + z2 = -2.5 + 0.25

Combine like terms:  + 0.25 = 1.25
1.25 + z2 = -2.5 + 0.25

Combine like terms: -2.5 + 0.25 = -2.25
1.25 + z2 = -2.25

Factor a perfect square on the left side:
(z + 0.5)(z + 0.5) = -2.25

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.