Solve the equation by completing the square: z^2 − 2z = 323

Question

A. -17, 19
B. -17, -19
C. 17, -19
D. 17, 19

Answer 1

To complete the square, we need to rearrange the equation by moving the constant term to the other side:

z^2 - 2z = 323
z^2 - 2z + 1 = 323 + 1
(z - 1)^2 = 324
(z - 1)^2 = 18^2

Now, take the square root of both sides:

z - 1 = ±18
z = 1 ± 18

Therefore, the solutions are:

z = 1 + 18 = 19
z = 1 - 18 = -17

So, the answer is A. -17, 19.