The product of two consecutive odd numbers is 399, what are the numbers?

1 Answer
Johnson Z.
Mar 3, 2016

solution set #1#: #19# and #21#
solution set #2#: #-21# and #-19#

Explanation:

#1#. Make #2# let statements to represent the variables to be used in the algebraic equation.

Let #color(red)x# represent the first number.
Let #color(blue)(x+2)# represent the second number.

#2#. Form an equation.

#color(red)x(color(blue)(x+2))=399#

#3#. Isolate for #x#.

#x^2+2x=399#

#x^2+2x-399=0#

#4#. Factor the quadratic trinomial.

#(x-19)(x+21)=0#

#5#. Set each factor to #0# to determine the possible values for #x#.

#x-19=0color(white)(XXXXXXXX)x+21=0#

#x=19color(white)(XXXXXXXXXX)x=-21#

#6#. Substitute #x=19,-21# into #color(blue)(x+2)# to determine the second numbers.

#color(blue)(x+2)color(white)(XXXXXXXXXXx)color(blue)(x+2)#

#=19+2color(white)(XXXXXXXX)=-21+2#

#=21color(white)(XXXXXXXXXX)=-19#

#:.#, the numbers are #19# and #21# or #-21# and #-19#.

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