## Total mechanical work, solving for x

1. The problem statement, all variables and given/known data

I understand the problem conceptually. I just need help solving for x, which is the hardest part of the problem for me.

1/2mv^2 = 1/2kx^2 + umgx

3. The attempt at a solution

Not really sure how to solve this. I tried and tried to separate by x but nothing worked. Here are 1 of the attempts I suppose. I feel pretty stumped here.

$$1/2mv^2 = 1/2kx^2 + umgx$$
$$1/2mv^2 - umgx = 1/2kx^2$$
$$\frac{mv^2}{k} - \frac{2umgx}{k} = x^2$$
???
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 Recognitions: Homework Help Looks like you've got a quadratic equation in x on your hands. Sound familiar?

 Quote by gneill Looks like you've got a quadratic equation in x on your hands. Sound familiar?
I thought a lot about how I couldn't expand x^2 + x.. but when you mentioned quadratic equation it came to me right now.. I'll get back to this once I get home.

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