Question

What number must you add to complete the square x^2+24x=17

Answer 1

We have
x² + 24x = 17                          (1)

Note that
(x + 12)² = x² + 24x + 144
By adding 144 to the left side of equation (1), it becomes a perfect square.

Therefore
x² + 24x = (x+12)² - 144         (2)

Substitute (2) into (1).
(x + 12)² - 144 = 17 
(x + 12)² = 17 +144
(x + 12)² = 161

Answer:
We added 144 to the left side of equation (1) in order to make it a perfect square.

Answer 2

The correct answer is 144