Question

How do you solve using the completing the square method `3x^2 + 11x – 20 = 0`?

Answer 1

`x=4/3` or `x=-5`

Explanation:

Premultiply by `12 = 3*2^2` to reduce the need to do arithmetic with fractions, complete the square then use the difference of squares identity:

`a^2-b^2=(a-b)(a+b)`

with `a=(6x+11)` and `b=19` as follows:

`0 = 12(3x^2+11x-20)`

`=36x^2+132x-240`

`=(6x)^2+2(6x)(11)-240`

`=(6x+11)^2-121-240`

`=(6x+11)^2-361`

`=(6x+11)^2-19^2`

`=((6x+11)-19)((6x+11)+19)`

`=(6x-8)(6x+30)`

`=(2(3x-4))(6(x+5))`

`=12(3x-4)(x+5)`

Hence `x=4/3` or `x=-5`