Question

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

Answer 1

The unknown number has the two values of 3 and 4

Explanation:

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`