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

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

$x=+3" and "x=+4$