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

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.