How Many Solutions Does the Equation x² - 4 = 0 Have?

When it comes to solving equations, you might come across the equation x² - 4 = 0 and wonder, "How many solutions does this have?" Well, settle in because we're about to break it down in a way that not only makes sense but might just make you giggle—or at least smile!

So, let's get into it. The equation x² - 4 = 0 is a simple quadratic equation. And, spoiler alert: it has two solutions! Surprised? Don’t be! Quadratic equations are known for having up to two solutions, and this one comfortably fits in that category.

Here’s the deal: if we rewrite it, we get x² = 4. To find the solutions, we take the square root of both sides. This takes us to two happy little solutions: x = 2 and x = -2. Yep, you read that right—two solutions popping out like a jack-in-the-box! So if you’re tossing around multiple-choice answers, the right pick is C. 2.

Now, let’s clear up some confusion that might arise from the other options. Option A suggests zero solutions, but that just doesn't apply here. You can’t have zero solutions when you've got x = 2 and x = -2 waving at you. As for Option B, saying there’s only one solution is simply off the mark. There are two, folks—so let’s keep our math hats on straight! Option D talks about three solutions, and here's the kicker: quadratic equations can never have three solutions. It’s like trying to swim up a waterfall; it just doesn’t work that way!

Understanding how we arrived at these solutions is key. By taking the square root of both sides, we're essentially working with the nature of squares. When you think about it, each positive real number has an associated negative counterpart. It’s kind of poetic, isn’t it? Just think: for every action, there’s a reaction—just like completing a square gives you two possible outcomes!

This principle is foundational not just for this equation but for solving many quadratic equations as you prepare for the College Algebra CLEP exam—or just tackle high school math! And these concepts will continue to help you as you move up the mathematical ladder. You know, just like a firm knowledge base allows better climbing, or something like that.

If you ever feel confused about mathematical principles or equations during your studies, take a breath and remember that every equation has its solutions waiting to be found. Some are easier than others, but with a bit of practice, you can navigate through them like a breezy summer day.

In summary, the equation x² - 4 = 0 indeed has two solutions: x = 2 and x = -2. It’s a nice, clean wrap-up that reinforces the beauty of mathematics—the elegance of quadratics, if you will. And hey, if you found this explanation relatable and straightforward, that's exactly the goal.

Ready to tackle more equations, or perhaps review some other key topics for the College Algebra CLEP exam? Keep that math brain buzzing and your spirits high—you're on a roll!