Question

Completely lost on square rooting a quadratic
x^2-8x+16=144. Don't I take 1/2 of the coefficient x^2-8x+4^2=144+2?

Answer 1

Do you want to find the roots?

Answer 2

Asked to solve using the square root formula.

Answer 3

The answer is -8 and 16, but I don't understand how to get there.

Answer 4

Factor that left hand side...what is a perfect square that comes out to

x² - 8x + 16 ?

(x .....)² ?

Answer 5

-4?

Answer 6

That might be a weird wording of it...here I'll help...

oh nvm you got it...so you have

(x - 4)² = 144

What would you do next using square roots?

Answer 7

subtract 16 from 144 which gives x^2-8x (x-4)^2=128

Answer 8

Nope....the 16 was in there when you factored the left hand side...remember

(x - 4)²

(x - 4) (x - 4)

x² - 4x - 4x + 16

x² - 8x + 16

It was in there...no all we have now is

(x - 4)² = 144

What you do next...is take the square root of both sides...

Answer 9

lost me with the 16...

Answer 10

I thought the x-4 was from dividing the coefficient 8x by 1/2.

Answer 11

Okay here.....what we wanted to do...was make it so we can use the square root property to solve this...

meaning we had to make your equation

x² - 8x + 16 = 144

look something like

(x - or + something)² = 144

Because what we do next is take the square root of both sides...

But we needed to find what that (x - or + something)² was

You're factoring that left hand side .....the x² - 8x + 16

and when you factor that...you get (x - 4)²

Answer 12

No....what you are describing ...is called "completing the square"...it is another way to solve quadratics..

No what your question wants...is to use square roots

Answer 13

Really hope I'm not confusing the crap out of you lol

Answer 14

Oh no, I was already there :) just really getting confused. I think I'm intersecting one way doing things with another.

Answer 15

Yeah....you're trying to use "completing the square" method when trying to understand the "square root" method lol

it would confuse anyone lol

Answer 16

I factor and get (x-1) (x+8)...what the heck am I doing here?

Answer 17

Lol okay lets try it 1 more time....you want to factor

x² - 8x + 16

So what 2 numbers multiply to get 16 AND add to get -8?

Answer 18

-4

Answer 19

Right...so what this would look like is

x² - 8x + 16

factors into

(x - 4) (x - 4)

Now it's dumb to write both of those when they're the same thing....so we write (x - 4)²

make sense so far?

Answer 20

yes...think I'm tracking on a short lead..

Answer 21

Okay...now just don't forget that right hand part of the equation...the 144 part

So we have

x² - 8x + 16 = 144

This is now turned into

(x - 4)² = 144

Okay? Because the x² - 8x + 16 has been factored...so it is replaced with the factor

Answer 22

x-4=12?

Answer 23

then solve for x?

Answer 24

GOOD! very close...but remember

\[\sqrt{144} = \pm 12\] right? because -12² = 144 too right?

Answer 25

so you actually have 2 equations to solve

x - 4 = 12
and
x - 4 = -12

NOW solve for each 'x'

Answer 26

16 and -8...good grief!

Answer 27

Haha this is why there are 2 other methods of solving these....lol this method is annoying! haha..

But good job! Stuck with it till the end!

Answer 28

care to walk me through another?

Answer 29

Lol if I can yes! And I'll try to explain it better

Answer 30

6x^2=25

Answer 31

I was leading with division first but that didn't work so well.

Answer 32

The answer is +- 5\[+- 5\sqrt{6}\div6\]

Answer 33

Oh see NOW comes the easy one! lol

Well it's not going to look pretty I'll tell you that

\[6x^2 = 25\]

Divide both sides by 6

\[x^2 = \frac{ 25 }{ 6 }\]

Now take your square root of both sides

\[x = \sqrt{\frac{ 25 }{ 6 }}\]

Now this can also be written as

\[x = \frac{ \sqrt{25} }{ \sqrt{6} }\]

so the only thing that can be simplified is √25...this is +/- 5 right?

so we have 2 answers

\[x = \frac{ 5 }{ \sqrt{6} }\]

and

\[x = \frac{ -5 }{ \sqrt{6} }\]

Answer 34

And okay...the only difference between MY answers and yours...is that YOUR answer...has the denominator rationalized...

Answer 35

That is what I did..so that is it? The denominator is rationalized? Why the heck doesn't the book explain that simple little thing that has been driving me crazy for the past hour!!??

Answer 36

This is done by multiplying both the top and the bottom of the fraction by √6...this cancels out the √6 on the bottom...so

\[x = \frac{ 5 }{ √6 } \times \frac{ \sqrt{6} }{ \sqrt{6} } = \frac{ 5\sqrt{6} }{ 6 }\]

and

\[x = -\frac{ 5 }{ √6 } \times \frac{ \sqrt{6} }{ \sqrt{6} } = -\frac{ 5\sqrt{6} }{ 6 }\]

Lol yeah that's it lol

Answer 37

And lol yeah books are good at that lol...well if that is what you did...Great job!

Answer 38

Geez...thank you for clearing that up for me.

Answer 39

No problem! Great job and even better job sticking with it and not giving up when you didn't understand it!

Answer 40

I have no choice. This is my last class before graduating. LAST CLASS!!!

Answer 41

Very thankful I found this site.

Answer 42

WOO! lol well keep going strong!

And yeah I found this site 2 months ago....It'll come in handy when I start calc 3 ...but for now...I'm just helping others lol

Answer 43

And I greatly appreciate that! Can you tell me what the medals are for that people offer up?

Answer 44

Medals is basically a reward "given by hitting the "Best Response" button to the side there" basically if you feel someone has helped you ...you give them a medal....And notice the little (24) near your name and the (81) near mine? That is called a smartscore....it goes up the more people you help...the more medals you get...the more questions you ask etc...

Answer 45

oh ok, got it! There you go!

Answer 46

Ahh, well thank you for that....as a matter of fact there YOU go *notice how your score just went from 24 to 26 now...

Answer 47

Yep! Thanks!

Answer 48

Well, gonna retire my brain for the evening. Need to unplug for a bit. Thank you for all your help!

Answer 49

No problem! Well you have a nice day / night depending on your time zone! lol

Answer 50

WA state :)

Answer 51

Ahh ...well have a nice night lol

Answer 52

You too