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

1 Answer
George C.
May 2, 2016

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

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