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math... factoring
ok i was gone from school two days this week, and im a little confused on my math homework. this is the problem im working on 4x^2+8x-21=0 ((^2=squared)).. my question is should i add 21 to both sides or just start factoring. i tried to just factor, and i could never get the signs to be write for everything. thanks
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Okay!! I know this is very late, but to just clear it up.. ^__^;;;;;
Okay, look for the factors of four which are (1*4) and (2*2).
Then look for the factors of 21 which are (1*21), (3*7)..
There are rules for this.. the rules are x^2 + 5x + 6 = 0... So, to factor this, it's (x+2)(x+3)=0. Notice the plus signs.
x^2 - 5x +6=0.. So, to factor this, it's (x-2)(x-3)=0.. Notice the minus signs...
x^2 + 5x - 6=0.. So, to factor this, it's (x+6)(x-1)=0.. Notice the positive and negative signs...
x^2 - 5x +6=0.. SO, to factor this, it's (x-6)(x+5)=0.. Notice the positive and negative signs...
In this case, it's (2x+7)(2x-3)=0.. Using the FOIL method.. (FOIL means, First term, Outside term, Inside term and Last term..) Using the distributive property, (2x)(2x) + (2x)(-3) + (2x)(7) + (7)(3).. So, multiplying that, 4x^2 - 6x + 14x -21.. Combining like terms.. 4^2 + 8x -21 =0.. Voila! The original equation!
So, since you factored (2x+7)(2x-3)=0, you can equate (2x+7)=0 and (2x-3)=0. YOu can only do this when it's equal to 0. GOt it? Okay.. Anyway, 2x+7=0.. To simplify that, 2x=-7 (you transpose +7 to the other side. It becomes negative and vice versa.) 2x/2=-7/2 (divide 2 in both sides because if you do one thing to one side, you have to do it to the other side too.) therefore, simplifying, x=-7/2.. So, that's one solution..
The other is 2x-3=0 so that's 2x=3, simplified to x=3/2.. that's the second solution..
therefore x=-7/2, 3/2.. Those are the two solutions... If you try to substitute it to the value of x, you will get 0..
Good luck! HOpe I explained it well.. More questions, just ask me.. ^__^ Sorry, if it's a bit late.. ^__^;;; I didn’t notice the question.. ^___^;;
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i'll take you through step through steps!
1. add 21 to each side 4x^2+8x-21+21=0+21
4x^2+8x=21
2. square the 4x 4x^2= 16x
16x+8x=21
3. add the two x's 16+8= 24x
24x=21
4. divide each side by 24 24x/24 = 21/24
x= 7/8th
hope i helped ya
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Okay I am pretty sure I have the right mehods and answers. Okay so like you need to add the 21 to both sides so then your new equation is 4x^2+8x=21
Then, pull out a 4x. So now your equation looks like this: 4x(x+2)=21
Now all that is left is to solve both for x. So you take 4x=21 which then becomes x=21/4 if left improperly or 5 1/4 if made into a mixed fraction. Then you take the x+2=21 and it becomes x=19.
So your two solutions are x=19 and x=21/4, or x=5 1/4. To double check that these solutions are right you can plug the answers in to the original equation (plug them in for x). If you get a true statement then you know they both work. Hope this helped :)
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