Solving x(5X+8)=4

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J_Barber

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Here's another one that has me stumped..

x(5x+8)=4

I want to multiply x by what's in the ( ) but it just doesnt seem right.

5x2+8x=4 that doesn't seem correct. Can I get a hint?
 
J_Barber said:
Here's another one that has me stumped..

x(5x+8)=4

I want to multiply x by what's in the ( ) but it just doesnt seem right.

5x2+8x=4 that doesn't seem correct. Can I get a hint?
Click to expand...
Do you know how to solve a quadratic equation in standard form?

\(\displaystyle 5x^2 + 8x = 4 \implies 5x^2 + 8x - 4 = 0.\)

Can you take it from here?
 
JeffM said:
Do you know how to solve a quadratic equation in standard form?

\(\displaystyle 5x^2 + 8x = 4 \implies 5x^2 + 8x - 4 = 0.\)

Can you take it from here?
Click to expand...

The ah ha moment!

5x2 + 8x -4
5x2 + 10x - 2x -4
5x(x + 2) -2(x + 2)
(x + 2)(5x - 2)

That right?
 
J_Barber said:
The ah ha moment!

5x2 + 8x -4
5x2 + 10x - 2x -4
5x(x + 2) -2(x + 2)
(x + 2)(5x - 2)

That right?
Click to expand...
Well not quite but you are thinking along the right lines. You have an equation; in fact you have a quadratic equation in standard form. You should have been taught at least three ways to solve such an animal.

\(\displaystyle 5x^2 + 8x - 4 = 0 \implies\)

\(\displaystyle (5x - 2)(x + 2) = 0.\)

Now if the product of two distinct numbers is zero, one or the other must be zero. This is called the zero product property.

So (as frequently happens with a quadratic equation) you have two possible answers, which are?
 
JeffM said:
Well not quite but you are thinking along the right lines. You have an equation; in fact you have a quadratic equation in standard form. You should have been taught at least three ways to solve such an animal.

\(\displaystyle 5x^2 + 8x - 4 = 0 \implies\)

\(\displaystyle (5x - 2)(x + 2) = 0.\)

Now if the product of two distinct numbers is zero, one or the other must be zero. This is called the zero product property.

So (as frequently happens with a quadratic equation) you have two possible answers, which are?
Click to expand...


Ok.. i get it now..

{2,-2} I just need to remember to work it all the way through.


Thanks!
 
mmm4444bot said:






What is "not quite"?
Click to expand...
Well he still has to solve the equation and the right hand side of that equation has disappeared.

So I could have said "Wrong."

But factoring the quadratic is an excellent way to solve the equation so I do not like to discourage by saying "Wrong," but be a bit encouraging. So out comes "not quite" because I cannot say "yes." It is what passes with me as pedagogy, of which I am completely ignorant. What is depressing is that even after doing the factoring, he got the solution wrong.
 
Why say "wrong", when the work shown is correct?

You read that post as a statement of his final answer?

(I'm sorry that you're depressed...)
 
mmm4444bot said:
Why say "wrong", when the work shown is correct?

You read that post as a statement of his final answer?

(I'm sorry that you're depressed...)
Click to expand...
Well, I did not say "wrong" despite the fact that the answer proposed to me as "right" is not right. He certainly did not indicate that he viewed his post as anything but a final answer. I think the fact that when he did propose something as a final answer it certainly was wrong indicates that he really did not fully understand what he was doing.

So I said "not quite." I am not sure why you think that was an unacceptable response. However, you are a moderator. I am happy to stop posting if that is what you wish.
 
lookagain said:
"I am happy to stop posting if that is what you wish." does not follow from "However, you are a moderator."


In fact, JeffM, you made a reply to mmm4444bot, as if it were an either/or situation about posting.

There is a continuum, whereby a moderator might critique a user, and then that user amends his post, asks a
question back to the moderator as a for instance, or possibly convinces the moderator that the thing which
was moderated about still has merit.
Click to expand...
No. I have no clue what is being objected to. Consequently, I have no clue what not to do in the future. As far as I am concerned, the answer was wrong because, at the very least, it was incomplete. Nevertheless, I gave a gentle reply because it seemed that the student was at least heading in the right direction. If I am being asked to stop doing something by a moderator and do not understand what is being objected to, I really have no choice but to stop posting. Now it is possible that I may be made to understand what is being objected to. I can then decide whether I want to continue posting under those restrictions.
 
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