Problem #5: Were you able to solve Problem 4? It's actually very hard to do without some guidance. Here's another hint. Try the substitution x = y - where k is a parameter to be determined. That is, make this substitution and find the value of k that eliminates the linear term. After making the substitution the problem will be given in terms of y, not x. That's OK. Solve the problem in this form, and substitute back to the original x variable at the end. Notice that after making our substitution we get: a y ka + 6 ( 1 - b ka + c =0. which is more complicated. Of course it is. We are still looking for the right substitution. Sometimes you have to complicate before you can simplify. Don't give up. Multiply everything out to see what you've got. Once you've found k make the substitution and eliminate the linear term - that was the goal, remember? At that point you should see the Quadratic Formula starting to emerge. Don't forget to unwind the substitution and solve for x It may interest you to learn that there is a Cubic Formula which solves the general cubic equation: ax + back + ca + d= 0. (1.5) just as the Quadratic Formula solves the general quadratic equation. 1 Aside: "Straightforward" is not the same as "easy."