Question

How do you solve using the completing the square method `8x^2 – 80x = –24`?

Answer 1

`x=5+sqrt22` or `x=5-sqrt22`

Explanation:

In `8x^2-80x=-24`, we have `8` as common factor. Hence dividing by `8`, we get `x^2-10x=-3`.

We can make the Left Hand Side of `x^2-10x`, a complete square by comparing it with `(x-a)^2=x^2-2ax+a^2` i.e. by adding square of half the coefficient of `x`.

As coefficient of `x` is `-10`, we need to add `(-10/2)^2=25`, to each side and then we have

`x^2-10x+25=25-3=22`

or `(x-5)^2=(sqrt22)^2`

Hence either `x-5=sqrt22` or `x-5=-sqrt22` i.e.

`x=5+sqrt22` or `x=5-sqrt22`