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

1 Answer
Apr 12, 2016

Answer:

#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#