How can you simplify the quadratic formula using completing the square?

  • Thread starter agentredlum
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In summary: The reason for the question is that the integral is not zero, because the log should be evaluated at the limits of integration and ln(-1) is not defined. Therefore, the statement is not correct.In summary, the conversation started with a request to share math tricks from all areas of mathematics. A trick was shared involving a quadratic formula, followed by another trick involving the value of i^i. There was then a discussion about the validity of the first trick, and a proof was shared for the existence of two irrational numbers whose product is rational. However, the proof was incorrect as the integral used was not zero and the statement was not true.
  • #281
Char. Limit said:
Wait... so all of this is to avoid minus signs?

Yeah, and here's the funny thing: they don't actually go away in practice.

Are people really that scared of a -4ac?
People in general? No.

Agenredlum? Apparently very much so.
 
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  • #282
agentredlum said:
Finally, but it took much more than half an hour LOL. That's because we're not in the same room talking.

I looked at what you wrote and I don't see a problem with it initially, except you put a b^2 where it didn't belong, but that doesn't matter to me because it did not affect your final result.

x = [b' +- sqrt(b'^2 + 4ac')]/[2a] = [(-b)^2 +- sqrt((-b)^2 + 4a(-c))]/[2a]

My mistake.

The rest of it seems fine to me but I must caution you, I am not as rigorous as others.

Yes, I have observed.

To me, it seems a tiny bit like circular reasoning but I am no expert in logic. Let othe

It only seems that way because the result is trivial.

Don't forget that the textbook version has an extra minus sign and subtraction instead of addition. Those 2 differences are going to cause more problems. Does that make sense?

No, that doesn't make sense. I would say that writting down a completely new equation, and then using that to solve the original one will cause problems. I'm a math guy, a minus sign doesn't scare me this much.
 
  • #283
Okay, you've spent long enough trying to repeal the use of negative numbers to recognize that all of the various forms of a quadratic equation differ only superficially. Time to wrap things up.
 
<h2>1. What are some examples of math tricks for everyone?</h2><p>Some examples of math tricks for everyone include the "11 Times Trick" for multiplying by 11, the "9 Times Trick" for multiplying by 9, and the "Finger Counting Trick" for multiplying by 9 or 6.</p><h2>2. How can math tricks benefit everyday life?</h2><p>Math tricks can benefit everyday life by making calculations faster and easier. They can also improve mental math skills and help with problem-solving in various situations.</p><h2>3. Are math tricks suitable for all ages?</h2><p>Yes, math tricks can be suitable for all ages. Some tricks may be more advanced and require a basic understanding of math concepts, but there are also simple tricks that can be taught to young children.</p><h2>4. Can math tricks be used in academic settings?</h2><p>Yes, math tricks can be used in academic settings. They can be helpful for students who struggle with math or for those who want to improve their mental math skills.</p><h2>5. Are there any downsides to using math tricks?</h2><p>One potential downside to using math tricks is that they may rely on memorization rather than understanding of mathematical concepts. This could lead to difficulties in more complex math problems that cannot be solved using a trick. It is important to also have a strong foundation in math principles.</p>

1. What are some examples of math tricks for everyone?

Some examples of math tricks for everyone include the "11 Times Trick" for multiplying by 11, the "9 Times Trick" for multiplying by 9, and the "Finger Counting Trick" for multiplying by 9 or 6.

2. How can math tricks benefit everyday life?

Math tricks can benefit everyday life by making calculations faster and easier. They can also improve mental math skills and help with problem-solving in various situations.

3. Are math tricks suitable for all ages?

Yes, math tricks can be suitable for all ages. Some tricks may be more advanced and require a basic understanding of math concepts, but there are also simple tricks that can be taught to young children.

4. Can math tricks be used in academic settings?

Yes, math tricks can be used in academic settings. They can be helpful for students who struggle with math or for those who want to improve their mental math skills.

5. Are there any downsides to using math tricks?

One potential downside to using math tricks is that they may rely on memorization rather than understanding of mathematical concepts. This could lead to difficulties in more complex math problems that cannot be solved using a trick. It is important to also have a strong foundation in math principles.

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