How to Factor Quadratic Equations with Two Variables?

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AI Thread Summary
To factor the quadratic equation y = x^2 - 8x + 10, the goal is to find two numbers that add to -8 and multiply to 10. The discussion highlights that simple factorization is not feasible, and the quadratic formula is necessary. Participants clarify the correct application of the formula, leading to the roots being expressed as (x - [8±√24]/2). The final values for x are approximated as 6.5505 and 1.4495 after reduction. The conversation emphasizes the importance of careful calculations and using tools like calculators for accuracy.
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I forgot How to do these...

Homework Statement



y = x^2 - 8x + 10
change into y = (x[plus or minus]A)*(x[plus or minus]B)

I just forgot how to do these... real fast could someone solve w/ showing work?

Thanks. I just don't remember how to do it...
 
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You need to find 2 numbers that give you the difference of -8 and the product of positive 10.

Since you won't be able to find it by simple factorization, you have to use the quadratic formula.

Google is your friend!
 
Oh ok thanks.

yea, i was just running factors over and over in my head and i wasn't coming up with anything, I'm kind of brain dead, so i wasn't sure if it was just me. Thanks.
 
1 and 10
2 and 5

:(
 
rocophysics said:
You need to find 2 numbers that give you the difference of -8 and the product of positive 10.

Since you won't be able to find it by simple factorization, you have to use the quadratic formula.

Google is your friend!

when i type in on Google quadratic formula, then i plug the equations in, it tells me x=16 and x = 8

? not the answer i need.
 
also those were wrong, i did it wrong. hold on
 
Nope ... try it again.
 
ok i think i got it, is it just (x - [8+\sqrt{24}/2]) * (x - [8-\sqrt{24}/2])?
 
MrNonexistent said:
ok i think i got it, is it just (x - [8+\sqrt{24}/2]) * (x - [8-\sqrt{24}/2])?
Yes, but don't forget to reduce!
 
  • #10
by that, you just mean plugging it into a calculator and finding the answer, correct?

which happens to be 6.5505 & 1.4495 correct?
 
  • #11
MrNonexistent said:
by that, you just mean plugging it into a calculator and finding the answer, correct?

which happens to be 6.5505 & 1.4495 correct?
No. \frac{8 \pm \sqrt{4 \cdot 6}}{2} can reduce.
 
  • #12
so 4 \pm \sqrt{2*3}?
 
  • #13
Yeppp.
 
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