z^2-4z+9=0

Solution for z^2-4z+9=0 equation:

Simplifying
z2 + -4z + 9 = 0

Reorder the terms:
9 + -4z + z2 = 0

Solving
9 + -4z + z2 = 0

Solving for variable 'z'.

Begin completing the square.

Move the constant term to the right:

Add '-9' to each side of the equation.
9 + -4z + -9 + z2 = 0 + -9

Reorder the terms:
9 + -9 + -4z + z2 = 0 + -9

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

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

The z term is -4z.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4z + 4 + z2 = -9 + 4

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

Combine like terms: -9 + 4 = -5
4 + -4z + z2 = -5

Factor a perfect square on the left side:
(z + -2)(z + -2) = -5

Can't calculate square root of the right side.

The solution to this equation could not be determined.