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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