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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!

Language:
English Language

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]

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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