Question

What number must be added to x2 – 5x to complete the square?

Answer 1

x² - 5x (given)

To complete the square, we need to add in "+(b/2)² - (b/2)² ", so in this case, it is "(5/2)² - (5/2)²":

⇒ x² - 5x + (5/2)² - (5/2)²

Now x² - 5x + (5/2)² can be put in a perfect square:

⇒ (x - 5/2)² - (5/2)²

Then we evaluate the term that is outside:

⇒ (x - 5/2)² - 25/4