Thread: Solving equations - missing solutions?

1. Solving equations - missing solutions?

I am advised that the following is incomplete, but I "cannot" see what is missing????

x^2 - 11x = 0
x^2 = 11x
x = 11

If I put x = 11 into the equation I get;

11^2 - 121 = 0

2. Re: Incomplete piece of work??????

You've lost a solution.

$x^2 - 11x = 0$
$x(x-11)=0$
$x = 0$ or $x=11$

Don't divide through by an unknown or this occurs.

3. Re: Incomplete piece of work??????

Write:
$x^2-11x=0$ as $x(x-11)=0$, this means there are two solutions. $x=11$ is one solution ( $11^2=121$), what's the other solution?

4. Re: Incomplete piece of work??????

Originally Posted by Quacky
You've lost a solution.

$x^2 - 11x = 0$
$x(x-11)=0$
$x = 0$ or $x=11$

Don't divide through by an unknown or this occurs.
Thanks for your help, I see it now I would end up with two solutions.

5. Re: Incomplete piece of work??????

It's a good solution if you want to check if your (algebraic) solution is right, anyway I think it's more important if you can solve equations then just use programs.

6. Re: Incomplete piece of work

Originally Posted by dalo
Hi David !

Have you considered using a math problem solver called Matamicus ?
It is a step-solver that can solve problems like the one you posted
and it produces a step-by-step solution of the problem. For instance,
the solution of your problem, produced by Matamicus, is shown below.
There is a free trial version of the program: Matamicus - math problem solver.
Thanks for the useful piece of software, I understand that some members on the forum would not agree with using software to solve problems, like any expert in a trade once you understand what you are doing why buy unnecessary tools, however in saything all that, for the novice who is learning from first principles and can't see mistakes until they are pointed out, it sounds like a good idea to me, kind of like having a maths teacher at your side.

7. Re: Solving equations - missing solutions?

Originally Posted by David Green
I am advised that the following is incomplete, but I "cannot" see what is missing????

x^2 - 11x = 0
x^2 = 11x
x = 11
How did you do this last step? You divided by x, right? But you cannot divide by 0 so what you should have is
"if $x\ne 0$ then x= 11". And, then, knowing that x= 0 has been excluded, put x= 0 into the equation to see if it is a solution.

If I put x = 11 into the equation I get;

11^2 - 121 = 0

8. Re: Incomplete piece of work

Originally Posted by David Green
Thanks for the useful piece of software, I understand that some members on the forum would not agree with using software to solve problems, like any expert in a trade once you understand what you are doing why buy unnecessary tools, however in saything all that, for the novice who is learning from first principles and can't see mistakes until they are pointed out, it sounds like a good idea to me, kind of like having a maths teacher at your side.
My opinion would be closer to this: you're not allowed to use software until you know what it's doing. Blindly using software packages is a great way to get your bridge to collapse.

9. Re: Solving equations - missing solutions?

Ackbeet:
My opinion would be closer to this: you're not allowed to use software until you know what it's doing. Blindly using software packages is a great way to get your bridge to collapse.
There is no need to use the program 'blindly'. There is a free trial version that enables you to test the program and see for yourself whether it is helpful to you or not. If you are not able to judge that by yourself, it would be wise to ask somebody who is able.

Siron:
It's a good solution if you want to check if your (algebraic) solution is right, anyway I think it's more important if you can solve equations then just use programs.
I agree with you Siron that it is more important to be able to solve equations without any help. If you are able to solve an equation, you can use the program just to check your solution. But if you are not able to solve it at all, the program can help you, just as somebody on this forum can help you.

The purpose of the program is not to solve equations instead of you (of course). But rather, you are supposed to learn something from the solution. So that next time you will be able to solve a problem of the similar type by yourself.

David:
...kind of like having a maths teacher at your side.
Exactly ! That is the very purpose of the program. Of course, the program can
never be as good as a real math teacher, but it is up to you to decide how successful it is.

I invite you all to test the free trial version and see for yourself whether the program can be of any use to you. If you are a very good mathematician (a math teacher for example) most probably you won't benefit from the program very much. But if you are a math student (high school or early college) quite probably the program can be helpful to you - sometimes it can show a way to solve a problem that you can't solve and sometimes you can check your solution or see another way to solve the problem that you are working on.

10. Re: Solving equations - missing solutions?

Originally Posted by dalo
Ackbeet: There is no need to use the program 'blindly'. There is a free trial version that enables you to test the program and see for yourself whether it is helpful to you or not. If you are not able to judge that by yourself, it would be wise to ask somebody who is able.
That's not really what I meant. I meant that if you don't know something of what the software is doing, how it is solving your problem, then you shouldn't use the software. How else are you going to know, for example, that your viewing rectangle for a graph is all wrong? Or that the cube root of a negative number that you found was wrong? Computers make fast, very accurate mistakes. They're also incredibly stupid: they do what you tell them to do, not what you want them to do. You absolutely must have some idea of the solution beforehand. There has to be a "sanity check" on the solution.

11. Re: Solving equations - missing solutions?

Originally Posted by dalo
Ackbeet: There is no need to use the program 'blindly'. There is a free trial version that enables you to test the program and see for yourself whether it is helpful to you or not. If you are not able to judge that by yourself, it would be wise to ask somebody who is able.

Siron: I agree with you Siron that it is more important to be able to solve equations without any help. If you are able to solve an equation, you can use the program just to check your solution. But if you are not able to solve it at all, the program can help you, just as somebody on this forum can help you.

The purpose of the program is not to solve equations instead of you (of course). But rather, you are supposed to learn something from the solution. So that next time you will be able to solve a problem of the similar type by yourself.

David:
Exactly ! That is the very purpose of the program. Of course, the program can
never be as good as a real math teacher, but it is up to you to decide how successful it is.

I invite you all to test the free trial version and see for yourself whether the program can be of any use to you. If you are a very good mathematician (a math teacher for example) most probably you won't benefit from the program very much. But if you are a math student (high school or early college) quite probably the program can be helpful to you - sometimes it can show a way to solve a problem that you can't solve and sometimes you can check your solution or see another way to solve the problem that you are working on.
This is not a free advertising site for comercial software. You could post information on your product once and metion it if someone asks about software. But you have posted at least five or six such free adds. If you do so again I will ban you and delete all your remaining posts, capiche?

CB