# Solving x = x(8-2x): My vs. Provided Solution

• emergentecon
In summary: This is a more general approach that doesn't require dividing by x (so you won't run into the issue of dividing by zero).
emergentecon

x = x(8-2x)

x = x(8-2x)

## The Attempt at a Solution

My Solution

x = x(8-2x)
1 = 8 - 2x
2x = 7
x = 7/2

Provided Solution

x = x(8-2x)
x = 8x - 2x^2
2x^2 -7x = 0
x(2x - 7) =
x = 0 / x = 7/2

Is my approach wrong?
Is x=0 always a possible answer, in addition to the found solution, so, should I have simply included x=0 in my solution?

Thanks!

Yes you would need to include x=0.

As your solution divided throughout by x, in doing so you limited your final answer as x could not be equal to zero (you can't divide by zero so x could be anything but zero).

1 person
emergentecon said:

x = x(8-2x)

x = x(8-2x)

## The Attempt at a Solution

My Solution

x = x(8-2x)
1 = 8 - 2x
2x = 7
x = 7/2

Provided Solution

x = x(8-2x)
x = 8x - 2x^2
2x^2 -7x = 0
x(2x - 7) =
x = 0 / x = 7/2

Is my approach wrong?
Is x=0 always a possible answer, in addition to the found solution, so, should I have simply included x=0 in my solution?

Thanks!

The red flag that should be a warning to you is that you are dividing both sides of an equation by a common unknown---x in this case. You should always check that you are not dividing by zero, as that is never, ever allowed. So, when you look at your original equation and before you start dividing, ask yourself: could I ever be dividing by 0? If the answer is yes, you can't do it. But, 0 is a perfectly legitimate solution: when x = 0 are the two sides of the equation equal to each other? The answer is yes.

After a while, this kind of checking will (or should) become second nature to you.

Notice that in the provided solution, they expanded the right side, and then brought all terms to the other side. After factoring the left side, they were able to find both solutions.

## 1. What is the difference between "My" and "Provided" solution?

The "My" solution refers to the solution that I have personally come up with, using my own methods and techniques. The "Provided" solution refers to a solution that has been given or provided by someone else, such as a textbook or online resource.

## 2. How do I know which solution is correct?

To determine which solution is correct, you can check your work by plugging the value of x into the original equation and seeing if it satisfies the equation. Additionally, you can compare your solution to the provided solution and see if they match.

## 3. Why are there sometimes multiple solutions to an equation?

Some equations may have multiple solutions because there are multiple values of x that can satisfy the equation. This is common in equations with exponents or variables on both sides of the equation.

## 4. Can I use different methods to solve an equation?

Yes, there are often multiple methods that can be used to solve an equation. It is important to choose a method that you are comfortable with and that will lead you to the correct solution.

## 5. How can I check if my solution is correct?

To check if your solution is correct, you can plug the value of x into the original equation and see if it satisfies the equation. You can also use a calculator or graphing tool to plot your solution and see if it intersects with the original equation at the given value of x.

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