I am working on a problem that asks me to solve for x for an iteration of the Lennard-Jones equation. Specifically, I am trying to determine the equilibrium separation between two hypothetical atoms. The equation is given to me as:
PE(x) = 2.3x10^-134 Jm^12/x^12 - 6.6x10^-77 Jm^6/x^6
I'm using MapleSoft 2015 to graphically represent this equation, and I was able to use the minimize function within MapleSoft to determine that the minimum of the graph occurs when PE= -4.734782609x10^-20 J
However, I am not certain how to get the x value at that point. My graphic calculator (a TI-84 Plus) won't recognize negative exponents beyond 1E-99 or so and it just give me an error any time I try to graph this equation, so I can get at the value that way.
I'm really green with MapleSoft; I'm sure there's a way to use the software to solve for x at a given f(x) value, but I don't know how. I tried using:
solve([equation], x) and got some answers, but they're all in the form of:
(some number) - (some number)I
I have no idea what that means so it doesn't help me and at any rate MapleSoft returned a number of solutions.
What I need to know is how do I go about solving for x? Could this be done as a quadratic equation with x = x^6? Please note, I'm not asking for anyone to give me the answer; I intend to do my own homework. I just need a method of getting at the answer that gives me results rather than frustration.
Edit: Here is the string of solutions Maple returns when I right click the equation and choose "solve":
{x = 2.977618011*10^(-10)-3.978806442*10^(-16)*I}, {x = 1.488812451*10^(-10)+2.578690850*10^(-10)*I}, {x = -1.488805560*10^(-10)+2.578694829*10^(-10)*I}, {x = -2.977618011*10^(-10)+3.978806442*10^(-16)*I}, {x = -1.488812451*10^(-10)-2.578690850*10^(-10)*I}, {x = 1.488805560*10^(-10)-2.578694829*10^(-10)*I}, {x = 2.977618011*10^(-10)+3.978806442*10^(-16)*I}, {x = 1.488805560*10^(-10)+2.578694829*10^(-10)*I}, {x = -1.488812451*10^(-10)+2.578690850*10^(-10)*I}, {x = -2.977618011*10^(-10)-3.978806442*10^(-16)*I}, {x = -1.488805560*10^(-10)-2.578694829*10^(-10)*I}, {x = 1.488812451*10^(-10)-2.578690850*10^(-10)*I}
What does it mean when "*I" is in the solution? Is this saying an imaginary number is the multiplier, i.e. sqrt(-1)?