explain answer to -X (10x^2 + 12x +2) = 0

[ugh...math]

Can someone please explain to me how the answer was figured to this problem?

-X (10x2 + 12x + 2) = 0

Answer: 0, -1/5, -1

(the 2 in 10x2 represents squared)

Any help will be greatly appreciated
__________________
Edited by stapel -- Reason for edit: clarifying "answer"

 

[tkhunny]

I'm not quite sure of what you wrote. You can use this guy "^" is signify exponentiation. x-squared would be x^2, for example.

You have already x = 0.

Factor out the common '2', leaving 5x^2 + 6x + 1 = 0
This is easily factored. (5x+1)(x+1) = 0

Can you finish?

 

[ugh...math]

Re: heeelllllllpppppp please

Here is the problem:

-X (10x^2 + 12x +2) = 0

The answer to the problem is:

0, -_1_ , -1
5


I am totally lost. I wish math would come to me naturally. Unfortunately, I missed that boat.

 

[ugh...math]

Re:

It's supposed to read -1 over 5. I'm not quite sure how to do that function

 

[pka]

The expression \(\displaystyle - x(10x^2 + 12x + 2) = 0\) is the same as \(\displaystyle x(5x^2 + 6x + 1) = 0\); is the same as \(\displaystyle x(5x + 1)(x + 1) = 0.\)

The roots of the latter are: \(\displaystyle \left\{ {0,\frac{{ - 1}}{5}, - 1} \right\}.\)

 

[galactus]

Try factoring.

You have:

\(\displaystyle \L\\x(10x^{2}+12x+2)=0\)

You can see that the x out front gives us the 0 as a solution.

Now, for the other 2 solutions:

Factor \(\displaystyle \L\\10x^{2}+12x+2\)

Because the coefficient of x^2 must be allowed for, we find two numbers which when added equal 12(the coefficient of x) and when multipled equal 20(because 2 is the constant and 10*2=20).

That would be 10 and 2. 10*2=20 and 10+2=12.

Group: \(\displaystyle 10x^{2}+10x+2x+2\)

\(\displaystyle (10x^{2}+10x)+(2x+2)\)

Factor:

\(\displaystyle \L\\10x(x+1)+2(x+1)\)...always make sure the terms in the parentheses are the same, otherwise, you won't get the right answer.

\(\displaystyle \L\\(10x+2)(x+1)\)

Factor out 2:

\(\displaystyle \H\\2(5x+1)(x+1)\)

There you have it. See your roots?.

Factoring just takes practice. Apply this technique to your next problem.

It may be roundabout but it's worth learning.

 

[ugh...math]

Re: heellllllppppppp

Thank you so much for your help! I'm amazed how easy math comes to some. I can't for the life of me figure out why nurses need to factor. I did however pass my IV meds calculation course with flying colors, so that shouldn't shake your confidence in nurses too much. Again, thank you for your help.

 

[tkhunny]

It's a common misconception, that math is about playing with symbols. Math also teaches you to organize your mind. That most certainly will come in handy for your patients.