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teach? dunno.... I can explain tho :)
it's like this:\[2x^2+3x-3=0\] kind of like foiling.
Yes, the opposite of foiling, the unfoiling if you will...
the easy way?
what I do is assume that I can factor and set it up like this: if there is a number in the front (that 2 there) use it for "a" in the following: (x ()/a) (x ()/a)
what's () ?
It is just something to fill in with a number we find.
(x ()/2) (x ()/2) is what I got so far. you with me?
the signs are still invisible, right?
yep, the equation actually tells us how to fill those in, but they are not important in step one.
ok. i'm understanding it a bit more
How is the last term inthe equation made? by addition or multiplication?
i converted sin of theta into X
X is not important yet; but that little (-3) at the end of your equation...how did it get there? was it (a)(b) = -3? or (a)+(b) = (-3)
the full equation from the textbook was: \[2\sin ^2 \theta+3\cos \theta-3=0\]
we will keep that in mind for later; but fer now, we need to KNOW how that (-3) got created. Was it by multiplication or addition?
it was from the textbook. it asks me to find the exact values in degrees
let me ask it this way; in order to "FOIL" to factors together to create the equation . The last term ther , that (-3) was made by some process. Was it by adding or multiplying.... think how to "unFOIL" this.
(x + y)(x + y) = xx +xy +xy +yy (x + y)(x + y) = x^2 +2xy +y^2 Is that last term there, that (y^2) made by adding or by multiply 2 numbers together?
umm.. it's plus and minus
y^2 = y+y ? or y^2 = y(y) ? (-3) = 1 + (-3)? or (-3) = (1)(-3)?
by unfoiling it, i get: \[(2\sin \theta- number)(\sin \theta + number)=0\]
I should probably clarify this: Do you want to know HOW to factor? or How to use the quadratic formula to find the answers?
i need to know how to factor the fastest way
the fastest way is to use the quadratic formula to find the solutions to a quadratic(a squared) equation.
quadratic is a fancy name for: the exponent value of "x" in this equation is a "2".
i meant i want to know how to factor. i'm left with those two numbers. which one should i pick.
Ill step you through how I do it :) which works if there are only inegers involved; otherwise, use the quad formula.
step1: multiply the first number and the last number to get your actual value that you need to factor to get 2 numbers. In this equation I would that would be: (2)(3) = 6. That is step 1.
step 2: setup your factoring into (x....()/a)(x.....()/a). For this equation that would be this: (x ( /2)) (x ( /2)) That is step 2:
step 3: look at the sign of the last term. In this case we have a (-3). If the sign is (+); I either need (+)(+) OR (-)(-) If the sign is (-) I need (+)(-) this sign of the last number tells me what I am going to use. In your case (-3) tells me that I am going to use (+)(-) step three is done.
step 4: What is the sign of the middle term? In this case we have (+3) This sign tells me that whichever numbers I pick; the largest one is this sign. If it is a (-) sign on the middle term; the largest number is (-) If it is a (+) sign on the middle term; the largest number is (+) In your case here; the sign of the middle term (+3) is (+); my biggest number will be positive. Step 4 is done.
step 5: fill in what I already know: (x + ( /2)) (x - (/2)) step 5 is done.
to clarify; in step 5 I used what I knew from YOUR equation that we are using. ok?
ok. i was wondering how to find the numbers. the rest is fine.
step 6: take the number we got back in step 1, or simply wait til now to get it :) remember we muliplied the first and last terms. (first)(last) (2)(3) = 6 we factor (6) to get our numbers. 1,6 2,3 Those are all I can get out of it... None of these will subtract to get (+3) 6-1 = 5 3-2 = 1 There is no way to use this method to factor your ORIGINAL equation. because we cannot get 2 number that work to fill in our missing stuff. End here and do quad formula.
ahh, i get it now. that's the answer i want. thanks heres the ipad link: http://on.fb.me/gJlBGl
there are going to be square roots involved; or maybe even no answer. But this method works for any integer value that can be found :)
whats an iPad contest?
kinda like a prize award?