How to Solve a Variable Cubed Equation

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Solving a variable cubed equation requires you to start by doing the inverse operation of addition or subtraction. Solve variable cubed equations with help from an experienced mathematics professional in this free video clip.

Part of the Video Series: Algebra
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Video Transcript

Hi, my name is Marija. I'm a mathematician, and today I'm going to show you how to solve variable cubed equations. So if I have an equation like two x to the third power minus two equals 14. OK like any other equation, I'm going to start by doing the inverse operation of addition or subtraction first to isolate the variable. So I'm going to do plus two on both sides. And when I do that, I get two x cubed, these cancel out, equals 16. Now like any other equation, I'm still trying to get x alone and I see that I have multiplication by it, so I'm going to do the inverse of multiplying, which is dividing. And when I do that, these twos cancel out, and I'm left with x cubes equals eight. Now x is not yet alone, this is where you come into the part where it's cubed. And the inverse of cubing a number is taking the cube root of that number. So what I'm going to do here is take the cube root of the left side. But if I do that I'll also have to take the cube root of the right side. So the cube root of x cubed is just x. The same way that the square root of x squared would have been just x. Equals the cube root of eight. So what this means is that I'm looking for a number that I multiply by itself three times to get eight. And if I think about it for a second, that number is two. Because two times two times two is eight. So my solution here would be x is two. So when you have a cube root equation, what you're going to do is isolate the variable until it's by itself with its exponent, and then take the cube root of both sides and you will solve your equation. My name is Marija, and I just showed you how to solve a variable cubed equation.


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