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Solving Quadratic Equations Using Square Roots - Concept
When graphing radical equations using shifts, adding or subtracting a constant that is not in the radical will shift the graph up (adding) or down (subtracting). Adding or subtracting a constant that is in the radical will shift the graph left (adding) or right (subtracting). Multiplying a negative constant by the equation will reflect the graph over the x-axis. Multiplying by a number larger than one increases the y-values.
When you're asked to solve a quadratic equation you have lots of options. One thing you can do is graph it and look for the x intercepts. You could try factoring and use a zero product property. You could use a quadratic formula. You can complete the square. Or you can do what we're going to look at here and that is taking the square root of both sides of an equation. This is a really useful technique in the following situation so listen up. If you don't hear anything else I hope you hear this.
Take the square root of both sides if you have no B term. What that means is that nowhere in your equation do you have something that has an X attached to it. You might have X squared, X to the third, or whatever but nothing has an X to the first power. Take the square roots of both sides if there's no B term.
I'll show you what I mean. Before we do that let's talk about what you know about square roots.
You guys know that four squared is equal to sixteen. It's kind of tricky because negative four squared is also equal to sixteen. So in our problems where we are solving by taking the square root of both sides sometimes you're going to get something like the square root of sixteen but be careful you're going to have a positive and a negative answer. The square root of sixteen is equal to four and also negative four.
So when you are doing problems like this and you are taking the square root of both sides in order to solve for X be really careful that you account for both positive and negative square roots.
The last thing I am going to leave you with is that this is different from that. Notice how here I have the negative sign under the square root sign. This has no real solution. So if you have something when you are solving where you have this square root of a negative number then that means that you're not going to have a solution, at least in this class. You'll get to those solutions in your future math class.
But for now if you have square root of a negative number you can just write "no real solution".