How do you Solve this?

2(x+3) - 2x^2(x+3) = 0

In my answer sheet they rewrite it to (x+3) * (2-2x^2) = 0

Im unsure what happens to the other (x+3)

Thank you in advance !

2(x+3) - 2x^2(x+3) = 0

In my answer sheet they rewrite it to (x+3) * (2-2x^2) = 0

Im unsure what happens to the other (x+3)

Thank you in advance !

Guest Mar 22, 2014

#1**0 **

How do you Solve this?

2(x+3) - 2x^2(x+3) = 0

In my answer sheet they rewrite it to (x+3) * (2-2x^2) = 0

Im unsure what happens to the other (x+3)

They (almost) took the greatest common factor, (x + 3), out of both terms......... !!!!

We can also take a "2" out !!!

Doing this, we get

2 * (x + 3) * (1 - x^2) = 0

We can get rid of the 2 by dividing through, so this becomes

(x + 3) * (1 - x^2) = 0

To solve, set each factor = 0

The first one is easy

x + 3 = 0

Subtracting 3 from both sides, we get

x = -3 and that's one solution

Now, setting the other factor to 0 we get

1 - x^2 = 0

This can be factored as

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

And setting these two things to 0 (as before), we get the other two solutions of 1 and -1

Hope this helps

2(x+3) - 2x^2(x+3) = 0

In my answer sheet they rewrite it to (x+3) * (2-2x^2) = 0

Im unsure what happens to the other (x+3)

They (almost) took the greatest common factor, (x + 3), out of both terms......... !!!!

We can also take a "2" out !!!

Doing this, we get

2 * (x + 3) * (1 - x^2) = 0

We can get rid of the 2 by dividing through, so this becomes

(x + 3) * (1 - x^2) = 0

To solve, set each factor = 0

The first one is easy

x + 3 = 0

Subtracting 3 from both sides, we get

x = -3 and that's one solution

Now, setting the other factor to 0 we get

1 - x^2 = 0

This can be factored as

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

And setting these two things to 0 (as before), we get the other two solutions of 1 and -1

Hope this helps

CPhill
Mar 22, 2014

#2**0 **

Hi Phida,

That is a good well presented question.

2(x+3) - 2x^{2}(x+3) = 0

Here is a slightly different question that might help you to understand.

Factorise this

2g - 2x^{2}g

The g is a common factor so it can be factorised to

g(2-2x^{2})

so

2 g - 2x^{2} g = g(2-2x ^{2})

Do you completely understand this? If not then let me know!

Now, in your question, it is not g it is (x+3) but it can still be factorised out in the same way.

2 (x+3) - 2x^{2} (x+3) = (x+3)(2-2x ^{2})

SO

2 (x+3) - 2x^{2} (x+3) =0

(x+3)(2-2x^{2}) = 0

If I had done it I would have factorised out the 2 as well but it doesn't matter.

Is that enough help do do you want some more?

Phida:How do you Solve this?

2(x+3) - 2x^2(x+3) = 0

In my answer sheet they rewrite it to (x+3) * (2-2x^2) = 0

Im unsure what happens to the other (x+3)

Thank you in advance !

Hi Phida,

That is a good well presented question.

2(x+3) - 2x

Here is a slightly different question that might help you to understand.

Factorise this

2g - 2x

The g is a common factor so it can be factorised to

g(2-2x

so

2 g - 2x

Do you completely understand this? If not then let me know!

Now, in your question, it is not g it is (x+3) but it can still be factorised out in the same way.

2 (x+3) - 2x

SO

2 (x+3) - 2x

(x+3)(2-2x

If I had done it I would have factorised out the 2 as well but it doesn't matter.

Is that enough help do do you want some more?

Melody
Mar 22, 2014

#3**0 **

I didn't know that you had already answered when I lodged mine Chris. The lodgement times are only 2 minutes apart.

There you go - great minds doing great things at the same time.

There you go - great minds doing great things at the same time.

Melody
Mar 22, 2014

#4**0 **

-----------------------------------------------------

Simpler to do it differently than your answer sheet

Divide both sides of the equation by 2 and you get (don't forget 0 divided by anything is 0)

(x+3) - x^2(x+3) = 0

Divide by (x+3) and you get

1 - x^2 = 0

Divide by -1 and you get

-1 + x^2 = 0

Add 1 to both sides of the equation and get

0 + x^2 = 1

x^2 = 1

x = 1

Phida:How do you Solve this?

2(x+3) - 2x^2(x+3) = 0

In my answer sheet they rewrite it to (x+3) * (2-2x^2) = 0

Im unsure what happens to the other (x+3)

Thank you in advance !

-----------------------------------------------------

Simpler to do it differently than your answer sheet

Divide both sides of the equation by 2 and you get (don't forget 0 divided by anything is 0)

(x+3) - x^2(x+3) = 0

Divide by (x+3) and you get

1 - x^2 = 0

Divide by -1 and you get

-1 + x^2 = 0

Add 1 to both sides of the equation and get

0 + x^2 = 1

x^2 = 1

x = 1

Guest Mar 22, 2014

#5**0 **

Hey radamus,

Thanks for your help on the answer,

However, I do have two remarks on your answer.

Primarily, x^{2} = 1 has two answers, both x = -1 and x = 1 since (-1) ^{2} = 1 is also correct

Secondly, you can't simply divide by (x+3) since for x = -3, you would be dividing by 0.

In your answer this means that the answer x = -3 was left out.

If you fill in x = -3 in the equation, you'll find that it is also correct.

**Off-topic**

To show you something fun which you can do by dividing by 0, here is a fallacious proof that 1 = 2

Step 1 Let a=b.

Step 2: Then a^{2} = ab,

Step 3: a^{2} + a^{2} = a^{2} + ab,

Step 4: 2a^{2} = a^{2} + ab,

Step 5: 2a^{2} - 2ab = a^{2} + ab - 2ab,

Step 6: and 2a^{2} - 2ab = a^{2} - ab

Step 7: This can be written as 2 ( a^{2} - ab) = a^{2} - ab,

Step 8: and cancelling the ( a^{2} - ab) from both sides gives 1=2.

Now in step 8, the mathematician divided by a^{2} - ab, but since a=b, a^{2} - ab = a^{2} - a^{2} = 0

That's why you should never divide by something which could be 0.

Reinout

radamus:Phida:

2(x+3) - 2x^2(x+3) = 0

In my answer sheet they rewrite it to (x+3) * (2-2x^2) = 0

Im unsure what happens to the other (x+3)

Thank you in advance !

-----------------------------------------------------

Simpler to do it differently than your answer sheet

Divide both sides of the equation by 2 and you get (don't forget 0 divided by anything is 0)

(x+3) - x^2(x+3) = 0

Divide by (x+3) and you get

1 - x^2 = 0

Divide by -1 and you get

-1 + x^2 = 0

Add 1 to both sides of the equation and get

0 + x^2 = 1

x^2 = 1

x = 1

Hey radamus,

Thanks for your help on the answer,

However, I do have two remarks on your answer.

Primarily, x

Secondly, you can't simply divide by (x+3) since for x = -3, you would be dividing by 0.

In your answer this means that the answer x = -3 was left out.

If you fill in x = -3 in the equation, you'll find that it is also correct.

To show you something fun which you can do by dividing by 0, here is a fallacious proof that 1 = 2

Step 1 Let a=b.

Step 2: Then a

Step 3: a

Step 4: 2a

Step 5: 2a

Step 6: and 2a

Step 7: This can be written as 2 ( a

Step 8: and cancelling the ( a

Now in step 8, the mathematician divided by a

That's why you should never divide by something which could be 0.

Reinout

reinout-g
Mar 22, 2014