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Current time:0:00Total duration:5:29

Solving square-root equations: two solutions

CCSS.Math:

Video transcript

let's say that we have the equation six plus three W is equal to the square root of 2w plus 12 plus 2w see if you can pause the video and solve for W and it might have more than one solution so keep that in mind alright now let's work through this together so the first thing I'd like to do whenever I see one of these radical equations just isolate the radical on one side of the equation so let's subtract 2w from both sides I want to get rid of that 2w from the right-hand side I just want the radical sign and if I subtract 2w from both sides what am I left with well on the left-hand side I am left with 6 plus 3w minus 2w well 3 of something take away two of them you're going to be left with W 6 plus W is equal to these cancel out we're left with the square root of 2w plus 12 now to get rid of the radical we're going to square both sides and we've seen before that this process right over here it's a little bit tricky because when you're squaring a radical in a radical equation like this and then you solve you might be involving you might find an extraneous solution what do I mean by that well we're going to get the same result whether we square this or whether we square that because when you square a negative it becomes a positive but those are fundamentally two different equations we only want the solutions that satisfy the one that doesn't have the negative there so that's where we're going to test our solutions to make sure that they're valid for our original equation so if we square both sides on the left hand side we're going to have well it's going to be W squared plus 2 times they're two times their product so 2 times 6 times W so it's 12 W plus 6 squared 36 is equal to now if you take the square root if you n square it you're going to be left with 2w plus 12 now we can subtract 2w and 12 from both sides so let's do that so then we can get into kind of a standard quadratic form so let's subtract 2w from both sides and let's subtract 12 from both sides so subtract 12 from the right subtract 12 here and once again I just want to get rid of this on right hand side and I am going to be left with I am going to be left with on the left hand side it's going to be W squared C 12 W minus 2 W is plus 10 w and then 36 minus 12 is plus 24 is equal to 0 and let's see to solve this I see is this factorable are there two numbers that add up to 10 and whose product is 24 well what jumps out at me is 6 and 4 so we can rewrite this as W plus 4 times W plus 6 is equal to 0 and so if I have the product of two things equaling 0 well to solve this either one or both of them could be equal to 0 0 times anything is going to be 0 so W plus 4 is equal to 0 or W plus 6 is equal to 0 and over here if you subtract 4 from both sides you get W is equal to negative 4 or subtract 6 from both sides here W is equal to negative 6 now let's let's verify that these actually are solutions to our original equation remember our original equation was 6 I'll rewrite it here our original equation was 6 plus 3 W is equal to the square root of 2 w plus 12 plus 2 w so let's see if W is equal to negative 4 if W is equal to negative 4 right over just a different is equal to negative 4 so that's going to be 6 plus 3 times negative 4 is equal to the square root of 2 times negative 4 plus 12 plus 2 times negative 4 so this would be this is negative 12 here this is negative 8 here this is negative 8 here so you have 6 plus negative 12 which is negative 6 is equal to the square root of negative 8 plus 12 is 4 plus negative 8 so that would be negative 6 is equal to 2 plus negative 8 which is absolutely true so this is definitely a solution and let's try W is equal to negative 6 so you is equal to negative six so we're going to get if we look up here we're going to have six plus three times negative six is equal to the square root of two times negative six plus twelve plus 2w so this is going to be negative 18 this is going to be negative twelve this is negative 12 negative 12 plus 12 is zero square root of zero this is all this zero and then two times and actually let me I shouldn't have written 2w they actually written two two times negative six so back to what I was doing this right over here is negative 18 and this is two times negative six plus twelve this is all zero square root of zero zero and then this is negative twelve so you get six plus negative 18 which is negative 12 is equal to zero plus negative 12 negative 12 which is absolutely correct so these are actually both solutions to our original radical equation