4Z^2-24Z+37=0

Solution for 4Z^2-24Z+37=0 equation:

Simplifying
4Z2 + -24Z + 37 = 0

Reorder the terms:
37 + -24Z + 4Z2 = 0

Solving
37 + -24Z + 4Z2 = 0

Solving for variable 'Z'.

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

Divide each side by '4'.
9.25 + -6Z + Z2 = 0

Move the constant term to the right:

Add '-9.25' to each side of the equation.
9.25 + -6Z + -9.25 + Z2 = 0 + -9.25

Reorder the terms:
9.25 + -9.25 + -6Z + Z2 = 0 + -9.25

Combine like terms: 9.25 + -9.25 = 0.00
0.00 + -6Z + Z2 = 0 + -9.25
-6Z + Z2 = 0 + -9.25

Combine like terms: 0 + -9.25 = -9.25
-6Z + Z2 = -9.25

The Z term is -6Z.  Take half its coefficient (-3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
-6Z + 9 + Z2 = -9.25 + 9

Reorder the terms:
9 + -6Z + Z2 = -9.25 + 9

Combine like terms: -9.25 + 9 = -0.25
9 + -6Z + Z2 = -0.25

Factor a perfect square on the left side:
(Z + -3)(Z + -3) = -0.25

Can't calculate square root of the right side.

The solution to this equation could not be determined.