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Solving Radical Equations 2159 Views
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Description:
To solve radical equations, you square both sides, FOIL it out if necessary, and simplify. Ta da!
Transcript
- 00:03
Solving radical equations, a la Shmoop. [Disco ball]
- 00:06
Your favorite underground electronica artist DJ UrchinX is spinning beats at a
- 00:11
secret location. He's left two clues both in the form of a radical expression. [DJ playing on a stage]
- 00:15
Solve them and you'll be one of the first people on earth to hear his new
- 00:20
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]
Full Transcript
- 00:26
plus 6 solve for X. First sqaure both sides to get rid of the square roots
- 00:31
leaving us with 3 x minus 2 equals x plus 6. Next add 2 to both sides and subtract [Chainsaw chopping through a log]
- 00:39
X from both sides, we get 2x equals 8 divide both sides by 2 and boom x equals 4.
- 00:47
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]
- 00:54
Square both sides to get rid of the square root on the left side and we get
- 00:59
3x plus 4 equals X minus 5 in parentheses squared. Now we're gonna
- 01:05
use foil on the right side, we can start by multiplying X by X which gives us x [Tin foil wrapped into a ball]
- 01:10
squared then we multiply X by minus 5 and we get -5x. We continue by
- 01:17
multiplying minus 5 by X we get minus 5x and we finish by multiplying minus 5 by
- 01:23
minus 5 which equals positive 25, our new equation now reads 3x plus 4 equals x
- 01:31
squared minus 10x plus 25. Subtract 3x and 4 from both sides and we
- 01:39
get x squared minus 13x plus 21 equals 0. Using the quadratic formula to solve for
- 01:48
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!']
- 01:54
minus 4ac (breathes in) all over 2a. We see that X equal 13 plus or minus the square root
- 02:02
of negative 13 squared minus 4 times 21 times 1 over 2. This simplifies into x
- 02:10
equals 13 plus or minus the square root of 169 minus 84 over 2. Therefore the
- 02:18
answer is x equals 13 plus or minus the square root of 85 over 2. Now it can't be
- 02:25
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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