z^2=2z-5

Solution for z^2=2z-5 equation:

Simplifying
z2 = 2z + -5

Reorder the terms:
z2 = -5 + 2z

Solving
z2 = -5 + 2z

Solving for variable 'z'.

Reorder the terms:
5 + -2z + z2 = -5 + 2z + 5 + -2z

Reorder the terms:
5 + -2z + z2 = -5 + 5 + 2z + -2z

Combine like terms: -5 + 5 = 0
5 + -2z + z2 = 0 + 2z + -2z
5 + -2z + z2 = 2z + -2z

Combine like terms: 2z + -2z = 0
5 + -2z + z2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-5' to each side of the equation.
5 + -2z + -5 + z2 = 0 + -5

Reorder the terms:
5 + -5 + -2z + z2 = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -2z + z2 = 0 + -5
-2z + z2 = 0 + -5

Combine like terms: 0 + -5 = -5
-2z + z2 = -5

The z term is -2z.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2z + 1 + z2 = -5 + 1

Reorder the terms:
1 + -2z + z2 = -5 + 1

Combine like terms: -5 + 1 = -4
1 + -2z + z2 = -4

Factor a perfect square on the left side:
(z + -1)(z + -1) = -4

Can't calculate square root of the right side.

The solution to this equation could not be determined.