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Maths Help (Algebra & Squared)

The Lovely Muffin

Hi,

Can anyone explain to me, in a simple/easy way, how to understand and do Algebra & Squared maths please?

I have always found them difficult. I have had plenty of people explain to me and I still don't understand.

I am in Leaving Cert (after being out of education for 3yrs) and I use the New COncise Maths 3 book.

Also,

Can anyone recommend a good calculator that can do squared + algebra please?

I currently have the Sharp el-531w and I can't do Alebra + Squared on it (cos I don't know how to) so I am looking for a calculator which is easier to use for Algebra + Squared.

Thanks for any help.

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LeixlipRed

When you say Algebra and Squared what do you mean exactly? It would help if you could be a little more specific so that people can offer advice and help

Overature

You should have a trawl through youtube as there are some very helpful videos on there.

you cant really do algerbra on any calculator, i used that calculator for the LC and found it fine. to square stuff just enter the number you want to square and press the x button with the little 2 to the top right of it.

sponsoredwalk

www.khanacademy.org

Start at the beginning of the videos and work your way through them &
you'll barely have to do any work in the leaving cert

The layout is a bit different & I think confusing so if you have any problems
just post a message here and let us know.

As for your message, It's a bit confusing but algebra and squaring would
probably be something like this.

x² = 9

Is that what is giving you trouble? If so, x² really just means x•x

I know that looks a bit confusing but the • means multiply!
Think of it this way:

3² = 3•3 = 9

In english, three squared is equal to three times three. This is equal to is 9.

If you think about it you'll see that

3² = 3•3 = three times three = 3 + 3 + 3 = 9.

Similarly 5² = 5•5 = 5 times 5 = 25 = 5 + 5 + 5 + 5 + 5

Now, when you see x² think x² = x•x = x + x + x + ...

We don't know how many x's there will be but if x = 2 then

x² = (2)² = x•x = (2)•(2) = 2 + 2 = 4

Similarly, if x = 7

x² = (7)² = x•x = (7)•(7) = 7 + 7 + 7 + 7 + 7 + 7 + 7 = 49

I feel sorry for you using that book, I remember looking at it a bit over a
year ago and being confused, my advice to you is to use the internet to
teach yourself mathematics :cool: Start with khanacademy.org

bnt

A note regarding calculators: that Sharp EL-531W can do all the stuff you want with numbers, but it's not going to do the algebra for you. (There are calculators that can do that - e.g. the TI-89 I have - but they're expensive, complicated to use, and illegal in exams.) The way it works in school exams, you do the algebra on paper, then plug in numbers if required. The examiner wants to see you do the algebra, not just write down the answer.

For example, if you want the roots of a polynomial like x²+2x-15=0, you use algebra to get (x+5)(x-3)=0, and therefore x = -5 and 3, and all without a calculator. But if the polynomial is not easily factored, such as 3x²-7x-43, you have to break out the quadratic formula, plug in the numbers and use the calculator. The Sharp can handle that kind of thing just fine.

The Lovely Muffin

Thanks for the replies everyone, I'll check out those links.

@ bnt[/URL] What brand is the TI-89 calculator? Have you a link to it please?

As for what I meant by Algebra and Squared;

Here are two examples:

Example one: 4x²-3x+8-3x²+5x-11

Example two: 2x-5x

Thanks again.

sponsoredwalk

Example one: 4x²-3x+8-3x²+5x-11

What about it? I think you want to know how to solve for x when

4x²-3x+8-3x²+5x-11 = 0

right?

Well what you do first is group the similar terms together:

4x²-3x+8-3x²+5x-11 = 0

(4x² -3x²) + (5x - 3x) + (8 - 11) = 0

4x² has degree 2 because of the ² in x².
5x has degree 1 because there is nothing like a ² or ³ ⁴ ⁵ etc...
8 has degree zero because there are no x terms.

(4x² -3x²) + (5x - 3x) + (8 - 11) = 0

x² + 2x - 3 = 0

Now, what you're trying to do is to find the value's that x will take on
in order to make x² + 2x - 3 really and truly equal to zero.
Notice that x² + 2x - 3 = 0 is the exact same as 4x²-3x+8-3x²+5x-11 = 0

Well lets play with x² + 2x - 3 = 0

set x = 1

(1)² + 2(1) - 3 = ???
1 + 2 - 3 = ???
3 - 3 = ???
0 = ???
so we see that ??? really is equal to zero!

Great! How about x = 2

(2)² + 2(2) - 3 = ???
4 + 4 - 3 = ???
8 - 3 = ???
5 = ???
So we see that ??? really equals 5.
Notice, that is not equal to zero!!!!

So most numbers you pick will not make the equation x² + 2x - 3 equal 0.

A better way to read this is:

set x = 1

(1)² + 2(1) - 3 = 0
1 + 2 - 3 = 0
3 - 3 = 0
0 = 0
so we see that 0 really is equal to zero!

Great! How about x = 2

(2)² + 2(2) - 3 = 0
4 + 4 - 3 = 0
8 - 3 = 0
5 = 0
But 5 isn't equal to 0 !!! So, x = 2 does not solve the equation!

Now, because of the x² it means that there are going to be two
numbers that make x² + 2x - 3 equal 0. We know that x = 1 already
gives us our answer, but there is one more. What is it?

We could try guessing numbers and solving equations like I've just done
above! But, what if you get an equation like

500x² + 414,860x - 9245670 = 0

You'll be guessing for quite a long time

Stick with x² + 2x - 3 = 0, there is a method of solving these equations
called factoring. Look at bnt's post, (s)he did it there already!
Check a book to learn this properly, or watch the videos on www.khanacademy.org or www.thinkwell.com (my advice!!!)
but we can make x² + 2x - 3 = 0 into the form

(x + _)(x + _) = 0

where _ & _ have to be found. I'll tell you the answer is

(x + 3)(x - 1) = 0

If we multiply this out by the foil method we will get our original equation
back!

x² + 2x - 3 = (x + 3)(x - 1) = 0

There is another really interesting thing here! Notice the (x - 1)
Well we already figured out that when x = 1 the equation is truly
equal to zero! Remember? So, here we have (x - 1) hmm...
The equation is saying (x + 3)(x - 1) = 0 so just take the
(x - 1) = 0 and notice that if
x - 1 = 0
x = 1

We have just discovered that by picking x = 1 we solve the eqation
without guessing! We have found a method to solve these things!
So, my guess is that by looking at (x + 3)(x - 1) = 0 again we notice
(x + 3) = 0
x + 3 = 0
x = - 3
is also a solution! Try it

So im sum:

4x²-3x+8-3x²+5x-11 = x² + 2x - 3 = (x + 3)(x - 1) = 0

are all equal! I really do advise the videos as they start from the beginning
and build up the logical foundation as to why you even want to do this!

Example two: 2x-5x

well I assume, again that 2x - 5x = 0

I want to be clear, 2x - 5x can be equal to a number other than 0!!!!

2x - 5x = 0
2x - 5x = 3
2x - 5x = 7
2x - 5x = a (where a is just a placeholder for any number you want!)

so if, say, 2x - 5x = 3 then:
2x - 5x = 3
- 3x = 3
- x = 1
x = - 1

If you want to see if this is true!

2x - 5x = 3
2(-1) - 5(-1) = 3
-2 -(-5) = 5
- 2 + 5 = 3
3 = 3

See!

Similarly, 4x²-3x+8-3x²+5x-11 can be equal to something other
than 0!!!

4x²-3x+8-3x²+5x-11 = 0
4x²-3x+8-3x²+5x-11 = 3
4x²-3x+8-3x²+5x-11 = 7
4x²-3x+8-3x²+5x-11 = a

In this case, say x = 5

4x²-3x+8-3x²+5x-11 = 5
(4x² -3x²) + (5x - 3x) + (8 - 11) = 5
(4x² -3x²) + (5x - 3x) + (8 - 11) - 5 = 0
(4x² -3x²) + (5x - 3x) - 3 - 5 = 0
(4x² -3x²) + (5x - 3x) - 8 = 0
x² + 2x - 8 = 0
(x + _)(x + _) = 0
(x + 4)(x - 2) = 0

You'll have to find out yourself how I did that last part via the books
or videos

bnt

Purple_Bobbin wrote: »

@ bnt[/URL] What brand is the TI-89 calculator? Have you a link to it please?

TI = Texas Instruments, here's a link. Current price on Amazon UK: £130-135. :eek:

Purple_Bobbin wrote: »

As for what I meant by Algebra and Squared;

Here are two examples:

Example one: 4x²-3x+8-3x²+5x-11

Example two: 2x-5x

What's the question, though - what are they asking you to do with them? In the second example, 2x-5x = (2-5)x = -3x, if you're being asked to simplify it. You can simplify the first example in a similar way by grouping together the x², x, and constants. Is that it, or are you being asked to solve for x?