Question
Solve the equation by completing the square: z^2 − 2z = 323
A. -17, 19
B. -17, -19
C. 17, -19
D. 17, 19
A. -17, 19
B. -17, -19
C. 17, -19
D. 17, 19
Answers
Answered by
GPT 3.5
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.
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.