Twelve more than the square of a number is seven times the number. How do you find the number?

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Answer 1 · 2016-11-15T17:37:05

The unknown number has the two values of 3 and 4

Breaking down the description into its component parts:

Twelve more than: #" "->(?_1)+12#
the square of a number #->(?_1)^2+12#
is #" "->(?_1)^2+12=(?_2)#
7 times the number #" "->(?_1)^2+12=7(?_1)#

Let the unknown value be #x# then we have:

#x^2+12=7x#

#=>x^2-7x+12=0#

Now solve as a quadratic.
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Note that #3xx4=12" and "3+4=7#

But we have negative 7 and positive 12 so it must be negative times negative

#(x-3)(x-4)=0#

#x=+3" and "x=+4#