Quadratic equation, factoring vs formula

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Dalmain

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Apr 15, 2021
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Good day all

Hope you are well

While doing a calculation it turned into a quadratic formula of x^2-x-5=0, I used the reverse FOIL method as some call it and factored to (x-3)(x+2)=0. I felt this was easier than using the formula, but the workbook shows to use the formula and gets very different answers. Where did I go wrong here? When must I factor and when must I use the formula and surely the formula and factoring should be the same answer?

Thank you in advance
 
Dalmain said:
While doing a calculation it turned into a quadratic formula of x^2-x-5=0, I used the reverse FOIL method as some call it and factored to (x-3)(x+2)=0. I felt this was easier than using the formula, but the workbook shows to use the formula and gets very different answers. Where did I go wrong here? When must I factor and when must I use the formula and surely the formula and factoring should be the same answer?

Thank you in advance
Click to expand...
What you did wrong was to factor incorrectly! Always check your factoring, by multiplying: If you expand (x-3)(x+2), you get x^2-x-6, not x^2-x-5.

Try again, and you'll find that it can't be factored; you have to use the quadratic formula (or, equivalently, complete the square).

I solve by factoring when I can easily factor. If I can't (or choose not to try hard), I use the formula. When you can factor, both methods give the same result. Of course, you can make mistakes either way! (The risk with the formula is that it's harder to check.)
 
(-3)+(2)=-1
(-3)(2)\(\displaystyle \neq - \cancel 6 \)5 ............................... corrected
 
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Ah, that was a silly mistake on my part. Thank you very much, Dr. Peterson and Steven G. It has been a long day.
 
Dalmain said:
Ah, that was a silly mistake on my part. Thank you very much, Dr. Peterson and Steven G. It has been a long day.
Click to expand...
I almost added, as I will now: 5 and 6 do that to almost everyone in factoring problems, at least once in their lives! You are not the first, and will not be the last.

Even @Steven G does it:
Steven G said:
(-3)+(2)=-1
(-3)(2)\(\displaystyle \neq\)-6
Click to expand...
He meant -5 there!
 
Dr.Peterson said:
I almost added, as I will now: 5 and 6 do that to almost everyone in factoring problems, at least once in their lives! You are not the first, and will not be the last.

Even @Steven G does it:

He meant -5 there!
Click to expand...
I need to spend some time in the corner thinking about these silly errors I make.
 
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