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Math and Arithmetic
Algebra
Factoring and Multiples

What two numbers add to be 6 and multiply to be negative 495?

Answer

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Wiki User
December 04, 2011 10:40PM

Mathematically, you are looking to answer the following system of equations:

x + y = 6

x * y = -495

This is rather simple.

First, determine x in terms of y:

x = 6 - y

Next, substitute for x in the second equation:

(6 - y) * y = -495

Now, solve for y:

6y - y2 = - 495

0 = y2 - 6y - 495

The solution to the above quadratic equation is:

y = (6 + sqrt(2016)) / 2

and

y = (6 - sqrt(2016)) / 2

reducing that further gives

y = 3+6*sqrt(14) or 3-6*sqrt(14)

Substituting back in to x=6-y, that means:

x = 3-6*sqrt(14) when y = 3+6*sqrt(14)

x = 3+6*sqrt(14) when y = 3-6*sqr(14)

Thus, the two numbers that satisfy your question are:

3+6*sqrt(14) or approximately 25.449944

and

3-6*sqrt(14) or approximately -19.449944