4Z^2-2Z=-9

Solution for 4Z^2-2Z=-9 equation:

Simplifying
4Z2 + -2Z = -9

Reorder the terms:
-2Z + 4Z2 = -9

Solving
-2Z + 4Z2 = -9

Solving for variable 'Z'.

Reorder the terms:
9 + -2Z + 4Z2 = -9 + 9

Combine like terms: -9 + 9 = 0
9 + -2Z + 4Z2 = 0

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

Divide each side by '4'.
2.25 + -0.5Z + Z2 = 0

Move the constant term to the right:

Add '-2.25' to each side of the equation.
2.25 + -0.5Z + -2.25 + Z2 = 0 + -2.25

Reorder the terms:
2.25 + -2.25 + -0.5Z + Z2 = 0 + -2.25

Combine like terms: 2.25 + -2.25 = 0.00
0.00 + -0.5Z + Z2 = 0 + -2.25
-0.5Z + Z2 = 0 + -2.25

Combine like terms: 0 + -2.25 = -2.25
-0.5Z + Z2 = -2.25

The Z term is -0.5Z.  Take half its coefficient (-0.25).
Square it (0.0625) and add it to both sides.

Add '0.0625' to each side of the equation.
-0.5Z + 0.0625 + Z2 = -2.25 + 0.0625

Reorder the terms:
0.0625 + -0.5Z + Z2 = -2.25 + 0.0625

Combine like terms: -2.25 + 0.0625 = -2.1875
0.0625 + -0.5Z + Z2 = -2.1875

Factor a perfect square on the left side:
(Z + -0.25)(Z + -0.25) = -2.1875

Can't calculate square root of the right side.

The solution to this equation could not be determined.