Can I Solve for c by Replacing b with a Value Greater Than 0?

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In summary, the conversation discusses solving for the value of c when b is replaced with any value greater than 0 in an equation. It is determined that there are two solutions for c, which are 20 and -20, depending on the value of b. The conversation then shifts to discussing a cask of wine and the possibility of drinking it in less than 20 days.
  • #1
mathland
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I replace b with any value greater than 0 and then solve for c. Right?

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  • #2
What do you get when you expand the LHS and equate the resulting terms with the corresponding terms in the RHS of the given equation
 
  • #3
Greg said:
What do you get when you expand the LHS and equate the resulting terms with the corresponding terms in the RHS of the given equation

Ok. I will do as you suggested and be back.
 
  • #4
It's been 7 months now! Are you still working on it?

For those who were wondering, there are two solutions.
(2x- b)(7x+ b)= 14x^2+ 2bx- 7bx- b^2= 14x^3- 5bx- b^2. That is to be equal to 14x^2- cx- 16.

So we must have -5b= -c and -b^2= -16. b^2= 16 so b= 4 or b= -4.
If b= 4, -5b= -20= -c so c= 20.
If b= -4, -5b= 20= -c so c= -20.

Check:
(2x- 4)(7x+ 4)= 14x^2+ 8x- 28x- 16= 14x^2- 20x- 16.
(2x+ 4)(7x- 4)= 14x^2- 8x+ 28x- 16= 14x^2+ 20x- 16.
 
  • #5
Beer soaked comment follows.
Country Boy said:
It's been 7 months now! Are you still working on it?
...
He's been banned permanently.
 
  • #6
I'll bet I could drink that cask of wine in less than 20 days!
 

Related to Can I Solve for c by Replacing b with a Value Greater Than 0?

1. Can I solve for c by replacing b with a value greater than 0?

Yes, you can solve for c by replacing b with a value greater than 0. This is because the value of b does not affect the ability to solve for c. As long as the equation is set up correctly, you can replace b with any value and still solve for c.

2. Why is it important to replace b with a value greater than 0?

Replacing b with a value greater than 0 allows for a more accurate and precise solution for c. This is because a non-zero value for b provides a better representation of the real-world scenario and can result in a more meaningful answer for c.

3. Can I replace b with a negative value when solving for c?

Yes, you can replace b with a negative value when solving for c. However, it is important to ensure that the negative value is appropriate for the given equation and situation. In some cases, a negative value for b may not make sense and could result in an invalid solution for c.

4. Is there a specific value that b should be replaced with when solving for c?

No, there is no specific value that b should be replaced with when solving for c. The value of b will depend on the specific equation and situation being analyzed. It is important to choose a value that makes sense in the context of the problem and will result in a valid solution for c.

5. Can I solve for c by replacing b with 0?

Yes, you can solve for c by replacing b with 0. However, this will only work if the equation is set up in a way that allows for b to be canceled out. In some cases, replacing b with 0 may not result in a meaningful solution for c and could lead to an invalid answer. It is important to carefully consider the equation and situation before replacing b with 0.

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