1. Solve by completing the square round to the nearest hundredth if necessary: "Well, I always try to complete the square, even though I'm still not sure why it's so squaresome. So, let's put our math shoes on and solve this one! The equation is 3x^2-6x-24=0. First, let's divide everything by 3, because why should 3 have all the fun? So we get x^2-2x-8=0. Now comes the fancy part, completing the square! We take half of the coefficient of x, square it, and add it to both sides. Half of -2 is -1, squared is 1, so we add 1 to both sides and we get x^2-2x+1-8+1=0+1. Simplify that mess, and we're left with (x-1)^2-7=0. Now, as a square, (x-1)^2 can never be negative, so if we want it to equal zero, -7 is the only option. But wait, it says round to the nearest hundredth! Silly instruction, there are no decimal points here. So the solution is x = 1, but the number doesn't get a decimal makeover this time."
2. What is the value of n such that the expression x^2+11x+n is a perfect square trinomial? "Ah, the perfect square trinomial. It's like the tricycle of polynomials, perfectly balanced and ready to roll. So, to make this expression a perfect square, we need to find the magic value of n. Here's the trick: take half of the coefficient of x, square it, and assign it to n. So, half of 11 is 5.5, 5.5 squared is 30.25. And voila, n = 30.25. Now, if only finding the perfect square n was as easy as finding the perfect slice of pizza..."
3. What is a solution of x^2+4x=96? "A solution? I've got a great solution for any problem - laughter! But let's solve this equation instead. We have x^2+4x=96. To find the solution, we need to balance this equation like a tightrope walker on a unicycle. We bring 96 to the other side, and we have x^2+4x-96=0. Now, let's put on our quadratic shoes and use that good old quadratic formula. x equals negative b, plus or minus square root of b squared, minus 4ac, all over 2a. You know, I think this quadratic formula could use some quadratic seasoning. Anyways, plug in the values and you get x = -12, 8. Ta-da! We solved it! And now we can go back to finding solutions to life's bigger mysteries, like why do we park in a driveway and drive on a parkway?"
4. Which of the following is a solution of x^2+14x+112=0? If necessary, round to the nearest hundredth. "Ah, the hunt for solutions! Will we find them? Or will we end up in a solution-less predicament? Only time will tell. So, let's take a look at x^2+14x+112=0. We've got a quadratic equation on our hands, ready to be solved like a puzzle. But the answer to this puzzle is no solution! That's right, my friend, no solution here. So, let's move on to bigger and better problems, like trying to understand why some superheroes wear their underwear on the outside. It's a mystery for the ages!"
5. A box shaped like a rectangular prism has a height of 17 in and a volume of 2720 in^3. The length is 4 inches greater than twice the width. What is the width of the box? "Ah, the joy of box dimensions! Let's unwrap this problem and see what's inside. We know the volume of the box is 2720 in^3, and the height is 17 in, but what about the width and length? Well, let's call the width 'W' and the length 'L'. Now, we know that the length is 4 inches greater than twice the width. So, L = 2W + 4. Now, let's put the pieces together. Volume equals length times width times height. Plugging in the given values, we have 2720 = (2W + 4) times W times 17. Now, get ready to solve this equation faster than a rabbit on roller skates. Simplify, divide, calculate, and finally, we find that the width is 8 inches. Hooray for boxes and their mysterious dimensions! Don't forget, boxes make great hiding spots for clowns like me!"