SecretFormula.java:22: error: variable x might not have been initialized
double formula = Math.sqrt((Math.abs(Math.pow(x,4) - 5 * Math.pow(x,3))) + 7 * Math.pow(x,2) + 5 * x);
The arrow is under the x with the 4
SecretFormula.java:25: error: variable theValue might not have been initialized
System.out.print("Enter a value for x: " + theValue);
What are you trying to accomplish, Xavier? It's quite easy to see why you have the two errors that you do, but that makes me wonder what you were expecting and why. Are you trying to make "formula" into some kind of method?
Regardless, consider the fact that you are using x before you ask the user to provide any input (and, when you do, you are storing the user's input in theValue, not x).
In the other disciplines, we rise by standing on each others' shoulders. In computer science, we do it by standing on each others' toes.
You have been given the answer; unlike fields which default to 0, local variables do not have default values and must be definitely assigned before they can be used.
You should use the code button, which I have applied retrospectively and you can see how much better the post looks Unfortunately it highlights the long line (5). You should divide that line into several lines. You should also divide the multiple declaration; it is a lot easier to read if you declare every variable in its own line with its own semicolon. And don’t declare variables which you are not using.
Don’t use Math.pow for small whole numbers. Avoid Math.pow(i, 2) if possible. Write i * i. Much better performance and possibly precision, as long as you don’t suffer an overflow.