ShmoopTube

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Solving radical equations, a la Shmoop. [Disco ball]

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Your favorite underground electronica artist DJ UrchinX is spinning beats at a

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secret location. He's left two clues both in the form of a radical expression. [DJ playing on a stage]

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Solve them and you'll be one of the first people on earth to hear his new

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music. Here's the first clue, square root of 3 X minus 2 equals square root of x [Equation written on a post-it note]

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plus 6 solve for X. First sqaure both sides to get rid of the square roots

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leaving us with 3 x minus 2 equals x plus 6. Next add 2 to both sides and subtract [Chainsaw chopping through a log]

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X from both sides, we get 2x equals 8 divide both sides by 2 and boom x equals 4.

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The next one's a little more complicated, square root of 3x plus 4 equals x minus 5. [Next problem written on a post-it note]

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Square both sides to get rid of the square root on the left side and we get

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3x plus 4 equals X minus 5 in parentheses squared. Now we're gonna

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use foil on the right side, we can start by multiplying X by X which gives us x [Tin foil wrapped into a ball]

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squared then we multiply X by minus 5 and we get -5x. We continue by

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multiplying minus 5 by X we get minus 5x and we finish by multiplying minus 5 by

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minus 5 which equals positive 25, our new equation now reads 3x plus 4 equals x

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squared minus 10x plus 25. Subtract 3x and 4 from both sides and we

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get x squared minus 13x plus 21 equals 0. Using the quadratic formula to solve for

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X is shown as x equals negative b plus or minus the square root of b squared [Man looks excited and says 'Look a cheatsheet!']

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minus 4ac (breathes in) all over 2a. We see that X equal 13 plus or minus the square root

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of negative 13 squared minus 4 times 21 times 1 over 2. This simplifies into x

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equals 13 plus or minus the square root of 169 minus 84 over 2. Therefore the

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answer is x equals 13 plus or minus the square root of 85 over 2. Now it can't be

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reduced any further just like your friends interest in going to this gig. [Woman looks happy that the problem is solved]

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