Total mechanical work, solving for x

[Nano-Passion]

Homework Statement

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

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.

$$1/2mv^2 = 1/2kx^2 + umgx$$
$$1/2mv^2 - umgx = 1/2kx^2$$
$$\frac{mv^2}{k} - \frac{2umgx}{k} = x^2$$
?

 

[gneill]

Looks like you've got a quadratic equation in x on your hands. Sound familiar?

 

[Nano-Passion]

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.