2z^2-6z+9=0

Solution for 2z^2-6z+9=0 equation:

Simplifying
2z2 + -6z + 9 = 0

Reorder the terms:
9 + -6z + 2z2 = 0

Solving
9 + -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'.
4.5 + -3z + z2 = 0

Move the constant term to the right:

Add '-4.5' to each side of the equation.
4.5 + -3z + -4.5 + z2 = 0 + -4.5

Reorder the terms:
4.5 + -4.5 + -3z + z2 = 0 + -4.5

Combine like terms: 4.5 + -4.5 = 0.0
0.0 + -3z + z2 = 0 + -4.5
-3z + z2 = 0 + -4.5

Combine like terms: 0 + -4.5 = -4.5
-3z + z2 = -4.5

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 = -4.5 + 2.25

Reorder the terms:
2.25 + -3z + z2 = -4.5 + 2.25

Combine like terms: -4.5 + 2.25 = -2.25
2.25 + -3z + z2 = -2.25

Factor a perfect square on the left side:
(z + -1.5)(z + -1.5) = -2.25

Can't calculate square root of the right side.

The solution to this equation could not be determined.