I need help with this ecvation!

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

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 ²(x+3) = 0

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

2g - 2x ²g
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?

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.

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

radamus:

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

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 a² = ab,
Step 3: a² + a² = a² + ab,
Step 4: 2a² = a² + ab,
Step 5: 2a² - 2ab = a² + ab - 2ab,
Step 6: and 2a² - 2ab = a² - ab
Step 7: This can be written as 2 ( a² - ab) = a² - ab,
Step 8: and cancelling the ( a² - ab) from both sides gives 1=2.

Now in step 8, the mathematician divided by a² - ab, but since a=b, a² - ab = a² - a² = 0

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

Reinout

Great demonstraton Reinout

What a great 'proof'. I like it.

I always suspected that 1=2