Rearrange This Expression Into Quadratic Form Ax2 Bx C 0
Hey there, math adventurers! Get ready to dive into a world of algebraic superpowers! Today, we're going to unlock a secret code, a magical transformation that turns all sorts of wacky expressions into something super organized and, dare I say, beautiful! We're talking about the legendary Quadratic Form, that elegant Ax² + Bx + C = 0. Think of it as the ultimate superhero costume for your math problems, making them look neat, tidy, and ready for action!
Imagine you've got a jumbled mess of toys all over your room. You've got action figures here, building blocks there, and a rogue sock hiding under the bed. It's chaos! But then, you decide to organize. You put all the action figures on the shelf, all the building blocks in a bin, and the sock… well, the sock eventually finds its way to the laundry hamper. Suddenly, your room looks amazing, right? Rearranging expressions into Ax² + Bx + C = 0 is kind of like that, but for numbers and letters!
So, what does this magical Ax² + Bx + C = 0 actually mean? It's a special kind of equation that has an x² term, an x term, and a plain old number, all lined up perfectly and set equal to zero. The A, B, and C are just placeholders for numbers. They can be positive, negative, fractions, or even whole numbers – they're the color choices for our superhero costume! The most important rule is that the A can't be zero, because then our x² would vanish, and it wouldn't be a quadratic anymore! That would be like trying to have a superhero without their signature cape – just not the same!
Let's say you're faced with an expression that looks like it's been through a blender. Maybe it's something like 3x² + 5 = -2x. At first glance, it might seem a bit overwhelming. It’s like seeing a single sock and knowing its partner is somewhere in the universe, but you have no idea where! But fear not, because we have the power to rearrange it! We want to get everything onto one side, so that glorious zero appears on the other.
Think of it like a game of "move the piece." Our goal is to gather all the x² terms, then all the x terms, and then all the regular numbers, and shove them all together, leaving a big, happy zero behind. So, in our example, 3x² + 5 = -2x, we see that -2x is chilling on the right side. We want it on the left, so we do the opposite! We add 2x to both sides. It’s like a friendly negotiation where everyone agrees to meet in the middle.
So,
3x² + 5 + 2x = -2x + 2x.Solved Rearrange this expression into quadratic form, ax2 + | Chegg.comBoom! Now we have
3x² + 2x + 5 = 0.
Isn't that fantastic? We've successfully transformed our jumbled expression into the dazzling Quadratic Form! We can now clearly see our A is 3, our B is 2, and our C is 5. It’s like our toys are all lined up in their designated spots, looking sharp and ready for whatever math challenges come their way!
What if things get a little more complicated? Maybe you have something like (x + 1)(x - 3) = 7. This looks like a secret agent mission, all mysterious and locked away. But again, we have our secret weapon: distribution! We need to multiply everything out to reveal the hidden terms.
Remember the FOIL method? First, Outer, Inner, Last? That's our trusty sidekick here!
(x * x) + (x * -3) + (1 * x) + (1 * -3) = 7Which gives us
x² - 3x + x - 3 = 7.Rearrange This Expression Into Quadratic Form Ax2 Bx C 0
Now, we combine the like terms. Those -3x and +x are like cousins who love to hang out together, so they become -2x.
x² - 2x - 3 = 7.
Almost there! We still have that pesky 7 on the right. We need to send it packing over to the left side. So, we subtract 7 from both sides.
x² - 2x - 3 - 7 = 7 - 7.And voilà! We get
x² - 2x - 10 = 0.
See? Even the trickiest expressions can be tamed! With a little bit of rearranging, a dash of distribution, and a whole lot of enthusiasm, you can transform any expression into the magnificent Quadratic Form. It's like giving your math problems a spa day – they emerge refreshed, organized, and ready to be solved! So go forth, my friends, and rearrange with glee! The world of Ax² + Bx + C = 0 awaits your brilliant touch! You've got this!