Math's Question (Again)
Discussion
grant.d said:
Hi There,
Can anyone give me a hand with this question?
(2x+3)=(2x+5)(2x-1)
If so can you please tell me how you get the answer and explain it if you can?
Many thanks,
Grant
(Perhaps thebluemonkey will be along shortly?)
Maths. Not math's.
Anyway,
2x+3=(2x+5)(2x-1) Multiply out the brackets ->
2x+3=4x^2-2x+10x-5 Tidy up the right hand side ->
2x+3=4x^2+8x-5 Subtract 2x+3 from both side ->
0=4x^2+6x-8
Put that into the quadratic formula which I hope you know...
If I remember correctly from GCSEs (a long time ago), to solve a quadratic of the form ax² +bx+c=0, you use the formula x=(-b+-√(b² -4ac))/2a
Therefore re-arrange your equation into 4x² +6x-8=0 and apply the above to get x=(-6+√164)/8 or x=(-6-√164)/8
i.e. there are always two answers to every quadratic equation.
Or something like that.
Lee
Therefore re-arrange your equation into 4x² +6x-8=0 and apply the above to get x=(-6+√164)/8 or x=(-6-√164)/8
i.e. there are always two answers to every quadratic equation.
Or something like that.
Lee
(2x+3)=(2x+5)(2x-1)
Multiply out the parenthesis: FOIL: First, Inside, Outside, Last
Combine like-terms, solve for x.
Meaning, multiply the first terms (2x times 2x = 4x^2), then multiply the inside terms (2x times 5 = 10x), then the ouside terms (2x times -1 = -2x), then the last terms (5 times -1 =-5). Now add the right hand side up (4x^2 + -2x +10x -5). On the left hand side, you have 2x + 3.
0= 4x^2 +6x -8
You can solve for x with the quadratic equation: -b +- ((b^2 -4ac)^1/2 )/2a where 4 is a, 6 is b, -8 is c. "Negative b plus or minus the square root of b-squared minus 4ac over 2a"
Or if you don't have a calculator (or aren't allowed one) you can use a technique called "completing the square":
Divide equation by 4 so that you have an x^2 term. Then you have
x^2 + (3/2)x =2
From your x term, figure out what you would need to complete the square, then add that to both sides, like this:
x^2 + (3/2)x + 9/16 = 2 + 9/16
then you have
(x + (3/4))^2 = 2 + 9/16
because (x+ 3/4)(x+ 3/4) = x^2 + 2(3/4)x + 9/16
any way, solve for x by taking the square root of both sides
x + 3/4 = (2 + 9/16)^1/2
so x = ((2 + 9/16)^1/2) - 3/4
Multiply out the parenthesis: FOIL: First, Inside, Outside, Last
Combine like-terms, solve for x.
Meaning, multiply the first terms (2x times 2x = 4x^2), then multiply the inside terms (2x times 5 = 10x), then the ouside terms (2x times -1 = -2x), then the last terms (5 times -1 =-5). Now add the right hand side up (4x^2 + -2x +10x -5). On the left hand side, you have 2x + 3.
0= 4x^2 +6x -8
You can solve for x with the quadratic equation: -b +- ((b^2 -4ac)^1/2 )/2a where 4 is a, 6 is b, -8 is c. "Negative b plus or minus the square root of b-squared minus 4ac over 2a"
Or if you don't have a calculator (or aren't allowed one) you can use a technique called "completing the square":
Divide equation by 4 so that you have an x^2 term. Then you have
x^2 + (3/2)x =2
From your x term, figure out what you would need to complete the square, then add that to both sides, like this:
x^2 + (3/2)x + 9/16 = 2 + 9/16
then you have
(x + (3/4))^2 = 2 + 9/16
because (x+ 3/4)(x+ 3/4) = x^2 + 2(3/4)x + 9/16
any way, solve for x by taking the square root of both sides
x + 3/4 = (2 + 9/16)^1/2
so x = ((2 + 9/16)^1/2) - 3/4
ifc63 said:Every one failed the honest way and then they scaled the marking so those who failed by the lowest margin passed?
Now in my day...
I’ve only ever seen it done once, with the scaling 2 people in a class of 30 passed structural analysis (without scaling no one would have passed). It’s like giving insolvable problems, its against modern teaching practices (Don’t ask me why, I’m not sure).
gasblaster said:
In my USA school they used to 'curve' marks, so if say the highest score in the class was 91%, they would increase that to 100% and then add 9 marks to everyone else's score too. Bizarre.
They do that because you can't use the same questions year in year out. What if one year the test was slightly harder then the year before? Thus, the top 5%, (or whatever) get the top grades. I actually think thats a fairer way of doing it.
Numbers just don't make sense to me 
gasblaster said:
In my USA school they used to 'curve' marks, so if say the highest score in the class was 91%, they would increase that to 100% and then add 9 marks to everyone else's score too. Bizarre.
I had that in my Higher Physics prelim.
I got 99.5% moved up to 100%
[/smuggitmode]
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