How do you find two consecutive, negative integers whose product is 156?

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Answer 1 · 2016-07-19T21:23:01

#-13 xx -12 = 156#

Let the two integers be #x and x+1#

Their product will be positive.

#x xx (x+1) = 156" "# this leads to a quadratic equation.

#x^2 +x -156 =0#

We need factors of 156 which differ by 1.

They will need to be very close to #sqrt156#, so lets start there.
#sqrt 156 = 12.4899#

#12 xx 13 = 156# which gives us exactly what we want.

#(x +13)(x-12) = 0#

#x = -13 or x = 12" "# reject 12 as we are looking for negative integers.

The integers are -13 and -12.