SAT Math: Changing Radicals into a Solvable Quadratic Equation

What value(s) of x satisfy the above equation?

Passport to Advanced MathOperations with rational expressions
Product TypeSAT Math
SATSAT Math
SAT MathNumbers and Operations
Passport to Advanced Math
Test PrepSAT Math

Transcript

00:20

all about overthrowing modern society And having everyone make a

00:23

living is a butter churn Er what can we do

00:25

to change this radical into something a little more civilization

00:28

friendly Well square both sides of the equation for one

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So let's just go do that thing And we've got

00:34

then to X minus five is the quantity x minus

00:37

four squared What Looks like we have a much less

00:39

anti social quadratic on our hands Now multiply out the

00:42

term on the right and then gather all the light

00:45

terms on one side of equations that gets us Was

00:48

that X square than minus Its foreign minus eight Acts

00:52

plus 4 square 16 Then we had to explain it's

00:54

five over here So let's just get that over here

00:57

Two zeros we're gonna add five there gets twenty one

00:59

then we're going to subtract two x here so it

01:02

gets is already on the ten X ofthe equation is

01:04

X squared minus ten x plus twenty one Oh I

01:07

see A three and seven Our future Now it's factoring

01:10

time So what is it while X minus three and

01:12

X minus seven right Well the solutions to this quadratic

01:15

equation are X equals three and seven rights Opposite sign

01:19

there That was negative SARS or positive which isn't the

01:22

correct answer See they would've fooled you with tea there

01:25

We don't want the solutions to this quadratic equation We

01:28

want the solutions to the radical equation we started with

01:32

So we have to plug in three to the original

01:34

equation though and no dear things go awry How so

01:38

While we get two times three that's six months five

01:41

is three months for a square root of one is

01:44

negative Once a one equals negative one How can that

01:47

be Yeah taking the square root of something I won't

01:50

ever give us a negative number So our only solution

01:53

is X equal seven So you've got to get rid

01:55

of the native one Just keeping a really well