That's presented to us in a slightly different way. So, these are the two possible x-values that satisfy the equation. And when x is equal to negative five, negative five plus three is negative two, squared is positive four, minusįour is also equal to zero. You substitute it back in if you substitute x equals negative one, then x plus three is equal to two, two-squared is four, minus four is zero. Substitute it back in, and then you can see when So, those are the two possible solutions and you can verify that. Negative two minus three is negative five. Or, over here we could subtract three from both sides to solve for x. Sides to solve for x and we're left with x isĮqual to negative one. So, if x plus three isĮqual to two, we could just subtract three from both If x plus three was negative two, negative two-squared is equal to four. Notice, if x plus three was positive two, two-squared is equal to four. And so we could write that x plus three couldīe equal to positive two or x plus three could beĮqual to negative two. Positive square root of four or the negative square root of four. Something right over here, is going to be equal to the If something-squared is equal to four, that means that the something, that means that this Three is going to be equal to the plus or minus So, one way of thinking about it is, I'm saying that x plus Way of thinking about it, if I have something-squared equaling four, I could say that that something needs to either be positive or negative two. And so now, I could take the square root of both sides and, or, another So, x plus three squared is equal to four. So, adding four to both sides will get rid of thisįour, subtracting four, this negative four on the left-hand side. This is I'm gonna isolate the x plus three squared on one side and the best way to do that To be equal to 12, which is absolutely true.The video and see if you can solve for x here. Root of 75 plus 6 is 81 needs to be equal to 12. Positive square root, for the principal square root. Have worked if this was the negative square root. That this actually works for our original equation. Let's see, it's 15, right? 5 times 10 is 50. On the left-hand side, we haveĥx and on the right-hand side, we have 75. When the original equation was the principal square root. And so that's why we have to beĬareful with the answers we get and actually make sure it works Have also gotten this if we squared the negative Root of 5x plus 6, you're going to get 5x plus 6. Square root of 5x plus 6 and we can square 9. Side right over here simplifies to the principal Lose the ability to say that they're equal. It on the left-hand side I also have to do it To get rid of the 3 is to subtract 3 from I want to do is I want to isolate this on You are only taking theĬheck and make sure that it gels with taking Information that you were taking the principal Square radical signs you actually lose the It to essentially get the radical sign to go away. On one side of the equation and then you can square To solve this type of equation is to isolate the radical sign Solve the equation, 3 plus the principal square root But he saved us the trouble of checking the original equation twice by saying "Principle Square Root" or, just the positive answer. So in the end you would've known that the correct answer is 15. But -15 would get all sorts of crazy (try it). If you plug in 15 back in the original equation it would check out. So if he hadn't said "Principle Square Root", then X could have been either -15 or 15. Plugging the negative or the positive numbers back in the original equation, you would get completely different results. If he had not mentioned Principle Square root, then your X's answer could be either a negative number or a positive of that number. Take for example the problem in this video. Because you literally don't know what the original number is and that is what you are solving for. This becomes important when dealing with roots of variables. So Principle square root of '4' is just '2'. The "Principle square root" means you don't care about the sign, and you are only dealing in the positive domain. What you don't know is whether that '2' was originally a '-2' or a '(positive)2'. So If you take the square root of a '4' you always get a '2' back. If you square the same number in negative form, like '-2', you also get a '4' (positive). If you square a positive number, like '2', you get '4' (positive).
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