The Zero Product Property
That changes the equation in our problem to this: 0 = 2x - 5 or 0 = x + 1, which now allows us to use the zero product property. The zero product property says that any time we multiply two things together and get zero, one of the things we started with must have been zero. That means that in this case either 2x - 5 = 0 or x + 1 = 0. Now it's only a few quick inverse operations to find that our two answers are 5/2 or -1.
x = -1 is a valid solution but doesn't make much sense for our game here. What we want to look at is our 5/2 answer, and it looks like we're a little bit off. We need to get a little more distance. Let's try leveling off our shot and see if that will give us the result you want. Just a little bit lower... okay. But remember, this is the final level, so our new equation probably isn't going to look any nicer than the last one, and sure enough, it's kind of crazy:
2x (3x - 5) = x + 30
This one isn't even equal to zero, but that's okay! We still need to do the same thing as earlier - use algebra to change this quadratic back to standard form. First multiplying with the distributive property, then using inverse operations to move everything to the left side of the equation, and finally combining like terms gives us our standard form quadratic equation 6x2 - 11x - 30 = 0.
The Quadratic Formula
Let's go ahead and use the quadratic formula for this one because the numbers are so much bigger than the last one. That means we have to first correctly identify a, b, and c as the coefficients on our trinomial. A, the first coefficient, is 6, the next one, b, is -11, and the constant on the end, c, is -30. We now need to substitute these values in to the formula, and now we need to follow the order of operations very carefully to come up with our two answers.
Working through this one step at a time, the - -11 will turn into a +11, the inside of the square root (what's called the discriminant) has an exponent that we can do first. -11 × -11 is 121. Then 4 × 6 × -30 is -720. Continuing the order of operations, doing the multiplication on the bottom (2 × 6) would give me 12. Doing a minus negative turns into plus a positive, which means we end up with 11 +/- the square root of 841/12, and it turns out the square root of 841 is 29, which means I can split the two answers up into 11 + (29/12) or 11 - (29/12). Doing that and then simplifying our fractions gives us our two answers, 10/3 or -3/2.
We can again more or less ignore our negative root here simply as what would happen if the slingshot broke and focus on the positive root at 10/3, which looks like it's going to work. I feel pretty confident going for this shot. Let's do it… and yes, we've got it! You have now beaten Furious Fowls. You are a solving quadratics expert and ready to solve any type of quadratic equation out there!