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

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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

Explanation:

Breaking down the description into its component parts:

Twelve more than: $\to (?_{1}) + 12$ $" "->(?_1)+12$
the square of a number $\to {(?_{1})}_{1}^{2} + 12$ $->(?_1)^2+12$
is $\to {(?_{1})}_{1}^{2} + 12 = (?_{2})$ $" "->(?_1)^2+12=(?_2)$
7 times the number $\to {(?_{1})}_{1}^{2} + 12 = 7 (?_{1})$ $" "->(?_1)^2+12=7(?_1)$

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

$x^{2} + 12 = 7 x$ $x^2+12=7x$

$\Rightarrow x^{2} - 7 x + 12 = 0$ $=>x^2-7x+12=0$

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

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

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

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

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

1 Answer

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