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

1 Answer
Shwetank Mauria
Apr 12, 2016

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

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