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TSI Math: Solving a Quadratic Equation through Grouping 2 Views


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Description:

Which of the following values is a root of the equation 10x² = 37x – 7?


Transcript

00:03

Okay yes i'm ass movers More quadratic ce in polly

00:06

and no meals here Which of the following values is

00:09

a root of the equation Ten x squared equals thirty

00:13

seven x minus seven Okay when you see these things

00:18

immediately quad ratify them so we're going to get negative

00:22

Ten x squared plus thirty seven x minus seven is

00:24

zero See we've zero fight it then we could use

00:27

the quadratic formula here but well we'll solve this equation

00:31

by grouping instead It's probably easier when the coefficient of

00:34

x squared isn't one like here It's ten or negative

00:37

ten Actually the first step is to multiply the coefficient

00:39

of x squared by the constant term Well here we

00:42

get negative ten times Negative seven which makes positive seventy

00:47

Now we need to think of two factors of this

00:49

result here for seventy which add up to thirty seven

00:52

So what could it be Yeah two times thirty five

00:56

is seventy and two plus thirty five is thirty seven

01:00

So pretty easy so we can rewrite This is thirty

01:02

seven x thing here is to Acts plus 35 acts

01:06

that'll help on the fact arising thing here So we're

01:09

then gonna factor to acts from the group to simplify

01:12

things a tad and we get well to x out

01:15

here that multiplies through the negative five x plus one

01:19

and then we've got the multiplying by negative seven times

01:24

the quantity negative five expose one equal zero we've got

01:26

negative five x plus one inside each parentheses here is

01:30

very clever very hard to dio Very hard to recognize

01:32

but hopefully you got it Okay so yes are factoring

01:35

was successful and now we're going to factor out the

01:38

negative five x plus one So we get that over

01:41

here on the left and then we're going to multiply

01:42

it by two x minus seven to get zero Well

01:45

the roots can be found by setting each of the

01:48

expressions in parentheses equals zero and just solving for x

01:51

Right So that gets us negative Five Acts plus 1

01:56

equals 0 and while we can subtract one from both

02:00

sides there we get negative five x equals negative one

02:03

Divide both sides by negative five and we get x

02:06

equals a fifth So whoa hold up That happens to

02:09

be be so we've technically found our answer However never

02:13

let it be said we don't finish what we start

02:15

to find the other route I'll do the same with

02:17

two x minus seven thereby adding seven on both sides

02:20

we get to act Sequel seven in the nexus seven

02:22

abs This is a positive value not the negative values

02:26

seen in negative seven halves there So give it up

02:30

either So the answer is b it's one fifth and 00:02:32.903 --> [endTime] that is in fact a route of that equation

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