WEBVTT
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Solve by taking roots
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So in this question, we must solve for đť‘Ą, finding đť‘Ą when weâ€™ve got three đť‘Ą squared minus nineteen equals two hundred and eighty-one.
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So what we want to do essentially is to get đť‘Ą on its own.
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So weâ€™re going to do the opposite of the order of operations.
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So first of all, we can see we can nicely and easily just get away that subtraction.
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And the way to get rid of a subtraction is you add.
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So weâ€™re going to have to add nineteen to both sides.
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Remember whatever you do to one side, you must do to the other.
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Adding nineteen to both sides will give us three đť‘Ą squared on the left-hand side.
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And that would be equal to two hundred and eighty-one plus nineteen which is three hundred.
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And then we can see that now on the đť‘Ą squared weâ€™ve got three multiplied by đť‘Ą squared.
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Well the opposite of times by is divide by.
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So getting rid of that first, weâ€™re going to have to divide both sides by three.
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As you must remember, whatever you do to one side we do it to the other.
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So now weâ€™ve got đť‘Ą squared is equal to one hundred.
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And this is the only bit thatâ€™s any different.
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So the bit that we need to be careful with is the opposite of square is square root.
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So here you can see itâ€™s đť‘Ą squared.
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So to get rid of the squared, we must square root both sides, giving us đť‘Ą equals, and we might be tempted to write just ten.
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But thatâ€™s not strictly true, because we know as weâ€™ve just done, we square rooted both sides.
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We know that ten times ten is equal to a hundred.
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That so is negative ten multiplied by negative ten.
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So when we square root, when we take roots, we have to put the answer as plus or minus, in this case ten.
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And we write it a little bit like that.
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So there we have it.
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We have solved this quadratic by taking roots.
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We just simply rearranged to make đť‘Ą the subject, well đť‘Ą squared the subject.
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And then we square rooted to get đť‘Ą the subject.
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Letâ€™s have a look at another quadratic thatâ€™s slightly different.
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Solve two multiplied by all of đť‘Ą plus four all squared equals one hundred and sixty two.
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So we can see the only thing we can get rid of away from the đť‘Ą side is this two multiplied by.
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We know the opposite of times by is divide by, so now we must divide both sides by two.
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This will give us đť‘Ą plus four all squared on the left-hand side and eighty one on the right.
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And now we have two options here.
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We can either take roots, which in this case weâ€™re going to do cause thatâ€™s what the video is about.
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Or we could know that đť‘Ą plus four all squared is the same as.
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And we could multiply out those brackets using foil.
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And then we could get a quadratic that we would be able to solve.
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Or if we couldnâ€™t factor it, then maybe we would use a quadratic formula.
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But in this case itâ€™s a lot quicker if we just take roots.
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So doing that on the left-hand side, we get đť‘Ą plus four.
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But the right-hand side, we end up with two options.
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We end up with nine or negative nine.
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Because weâ€™ve just shown in the example before if weâ€™ve got negative nine and we multiplied it by negative nine, we get positive eighty-one.
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And then if we have nine And multiplied it by nine, we also get positive eighty-one.
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So square rooting the eighty-one gives us plus or minus nine.
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And now we have two options for a root.
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We have an option where the nine is positive and we have one for where itâ€™s negative.
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So in the case where it is positive, weâ€™ve got nine and then we take away four.
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And we know that nine take away four is just five.
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And in the case where itâ€™s negative, weâ€™ve got negative nine take away four.
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And negative nine take away four is equal to negative thirteen.
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So there we have it.
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We have solved by taking roots for this quadratic.
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And itâ€™s a lot simpler than as we said multiplying out the brackets and then putting it into a quadratic and finding out if we can factor it or not.
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In this case, itâ€™s a lot easier just to take roots.
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But the most important thing is remembering that plus or minus when we square root.