What two numbers multiply to get -150 and add to 5?

Answer 1

-145

Answer 2

So this kind of problem is fun. To solve it, first we want to take the information you have, and write it in the form of equations. We know we are looking for two numbers, so lets call them X and Y.

Now we know that you want the two numbers when mulitiplied to equal -150 so the first equation is: X * Y = -150

We also know that we want the sum of the nujmbers to equal 5 so the second equation is: X + Y = 5

Now, just a quick trick, when two numbers are multiplied together, and the result is negative, exactly one of the original numbers must be negative.

So the good news is that we have two equations, and two variables, which means we can solve for them.

Lets try re-writing the second equation as X = 5 - Y and plug it into the first equation. This gives us (5 - Y) * Y = -150

We need to solve this, so first we mulitiply the Y through to get: 5Y - Y^2 = -150

Simplifying this, we get a quadratic equation Y^2 -5Y - 150 = 0

To solve that, you need to use the quadratic equation, and we find that the only number which works for Y is -10. (Note (-10 * -10) - 50 * -10 - 150 = 0).

Now we can take this knowlege of Y and use the second equation to solve for X

X + Y = 5 and we know that Y = -10

Thus X -10 = 5 which is the same as X = 15

If we check, you'll notice that -10 * 15 = -150 and -10 + 15 = 5

So your two numbers are -10 and 15. This problem was kind of tricky because normally when you solve systems of equations (what we did when we had two variables and two equations and solved for their values) usually you don't need to worry about quadratic equations.