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MonchangerFlag for United States of America

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Finding solutions to a quadratic equation by factoring

I'm going over my algebra so I can finally go to college. There's this one issue that I never really understood back in high-school:

When you have an quadratic equation, we were taught that you can solve it by using factoring.
My problem is that to factor, the book I have just tells you to *guess* two numbers that add up to equal x and multiply to equal y.

For example:
x*x - 11x + 28 = 0
can be converted to:

(x-4)(x-7) = 0
where you can solve it easily.

Isn't there a better way than guessing them? What would you do with seven-digit or non-integer numbers?

(When I tried solving the set of equations of:
m * n =  28
m + n = -11
I just got back to the original quadratic function- just with the m instead of x)

Don't mathematicians have a better method to do this? Math just always seemed the last place where guessing is the way to solve problems.

Monchanger
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Victor_R

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Thanks! And especially thanks for the URL. I love getting an explanation of how the formula works.

Now I only have to figure out a way to memorize that whole thing :-P

Monchanger
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Victor_R

Very welcome. Thanks for the A!

Let me know if you have more questions.