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Current time:0:00Total duration:4:25

Solving quadratics by taking square roots: with steps

Video transcript

use the cards below to create a list of steps in order that will solve the following equation three times X plus six squared is equal to 75 and I encourage you to pause this video now and try to figure it out in your own figure out which of these steps and in what order you would do to solve for X here so I'm assuming you've given it a go so let's try to work through it together and first let me just rewrite the equation so we have 3 times the quantity X plus 6 squared is equal to 75 so what I want to do is I want to isolate the X plus 6 squared on the left hand side or another way of thinking about it I don't want this 3 here anymore so how would I get rid of that 3 well I could divide the left-hand side by 3 but if I do that to only one side of the equation it won't be equal anymore these two things in yellow were equal to each other if I want the equalities to hold anything that I do to the left-hand side I have to do to the right-hand side so let me divide that by 3 as well and so on the left-hand side I am left with X plus 6 squared is equal to 75 divided by 3 so 75 divided by 3 is 25 now if I told you that something squared so actually let's let me just pick out the first one I did I divided both sides by 3 so that was my that was my first step there let me write that in a darker color so that was my first step right over there now let's think about what we're doing we're saying that something squared we're saying that something squared is equal to 25 so this something could be the positive or negative square root of 25 so let's take thee so we could write this as X plus 6 is equal to the plus or minus square root of 25 so I'm essentially taking the positive and negative square root of both sides so let's see this looks like this step I took the square root of both sides that's step number 2 and so let me just rewrite this this is the same thing as X plus 6 is equal to plus or minus 5 and I want to I want to just have an X on the left-hand side I want to solve for X that's the goal from the beginning so I would like to get rid of this I'd like to get rid of this six well the easiest way to do that is to subtract six from the left-hand side but just like before I can't just do it from one side of an equation then the Equality wouldn't be true we're literally saying that X plus six is equal to plus or minus five so X plus six minus six is going to be equal to plus or minus five minus six or actually when we write it this way so let me subtract six from both sides on the left-hand side I'm left with an X and on the right hand side I have and I could write it this way negative six let me do it in that green color I have negative six plus or minus plus or minus five so what are the possible values of X or actually I keep forgetting I we don't have to actually give the value for X we just have to say what steps we did so then let's see after we took the square root of both sides we then subtracted 6 from both sides so that was step three right over there then they got that got us to essentially the two possible X's that would satisfy this equation right over here and just for fun let's actually solve it all the way so if we solve it all the way we get two so X is equal to negative six plus five is negative one or X is equal to negative six minus five is negative 11 and you could verify but that both of these work if you put either of em in here if you put negative one here you get negative one plus six squared is 5 squared if you put negative 11 here it's negative 11 plus 6 is negative 5 squared obviously either plus or minus five squared is going to be 25 25 times 3 is 75 so these are our three steps we divided both sides by 3 subtract it then we took the square root of both sides then we subtracted 6 from both sides and then we were essentially done so let's input those steps so the first thing we do it would divide both sides by 3 that's the first thing we did then we took the square root of both sides and then we subtracted 6 from both sides we got it right