Bungee Jump: Conservation of Energy

[teme92]

Homework Statement

A bungee jumper of mass m drops off a bridge and falls vertically downwards. The bungee cord is elastic with natural length L and stiffness k. Deduce that at the lowest point of the fall, the cord is stretched by an amount:

x=mg/k(1+√(1+(2kl/mg))

Homework Equations

F=-kx
PE=mgh=0.5kx²

Where h=L+x

The Attempt at a Solution

The total energy before the jump is equal to the total energy after the jump. Since at the bottom there is no kinetic energy I said the Potential Energy before is equal to the Elastic Energy at the bottom.

So:

mg(L+x)=0.5kx²
x²=(2mgx +2mgl)/k
x=√((2mgx +2mgl)/k)

I'm having problems here trying to get in the asked form. Have I forgotten something n the conservation of energy?

 

[willem2]

There's an x on the right hand side of the equals sign in your final answer.
The line above that is a quadratic equation.

 

[teme92]

So does that mean I have to solve it quadratically?

 

[willem2]

So does that mean I have to solve it quadratically?

I suppose you know how to solve a quadratic equation. ax^2 + bx + c = 0 ?