Question

How do you solve `x^2 - 6x = 391` by completing the square?

Answer 1

`x=23` or `x-17`

Explanation:

In `x^2-6x=391` as the Left Hand Side is `x^2-6x`, we can make it a complete square (compare it with `(x-a)^2=x^2-2ax+a^2`) by adding **square of half the coefficient of `x`.

As coefficient of `x` is `-6`, we need to add `(-6/2)^2=9`, to each side and then we have

`x^2-6x+9=391+9=400`

or `(x-3)^2=20^2`

Hence either `x-3=20` or `x-3=-20` i.e.

`x=23` or `x-17`