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

 Passport to Advanced Math Operations with rational expressions Product Type SAT Math SAT SAT Math SAT Math Numbers and OperationsPassport to Advanced Math Test Prep SAT 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

00:31

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