Solving Radical Equations - Problem 2
I always want to undo what’s being done to x when I’m solving an equation. So in this situation, there’s a lot that’s being done to x. Not only is x under a square root sign, but that whole square root is being multiplied by 2, it has this -1 business. I have to go through step by step and undo each one of those pieces. A lot of students at this place in the very beginning are tempted to do something funny like distributing with 2 or something, don’t do that. What you want to do is undo step by step what’s been done to the x, isolate the square root and then square both sides.
So the first thing I’m going to do is add 1 to both sides to get rid of that -1 piece. Okay, next thing I’m going to do is divide both sides by 2 so that I no longer have that square root being multiplied by 2. I’ll just have the square root of 3x plus 7 equals 4. By the way please be really careful with how you write this. Don’t stop your square root bar like that or else you’re going to make a mistake. Remember the whole quantity 3x plus 7 is square rooted, so you have to have that bar go all the way across the top.
Okay, now that my square root is isolated I’m going to undo the square root which is squaring both sides. A lot of students get confused, a lot of students will say this, they’ll say 3x plus 7 is equal 2, do you see what I did wrong? What this person did is they square rooted 4 instead of squaring 4. It’s really tricky. If it helps you write out squared, that will help you to see that 3x plus 7 is supposed to be equal to 16. From there you guys know how to solve for x. It’s really straight forward and you get x is equal to 3.
Let me make sure I check my solution. The way to check is to take 3 and substitute it back up in there and see if when I evaluate, I do get the answer 7. So let me try that I’m going to back up a little bit so I have more space. 2 times the square root of 3 times 3 plus 7 take away 1, oops I hope is equal to 7. Okay so that’s 2 times the square root of 9 plus 7 is 16, square root of 16 I know is 4, 2 times 4 is 8 take away 1, good that is equals to 7. So I know I did that problem correctly.
Again guys if you couldn't remember the general process is to isolate the square root, that’s what all of this was, and then square both sides of the equation, you’ll be able to solve for x. And always check your work. There’s no reason why you want to turn in wrong homework. Plus if you check your work and you got something wrong, that helps you identify what questions you should ask your teacher or your tutor.