Question

Here's one more that I need the steps to not the answer, If I can get the steps I can get the answer, thanks.

Given the quadratic function f(x) = x2 – 12x + 36, find a value of x such that f(x) = 9.

Answer 1

f(x) = x^2 - 12x + 36 AND f(x) = 9

since f(x) = f(x) we can therefore say that x^2 - 12x + 36 = 9

Answer 2

Thank you. I just factor from there to solve correct?

Answer 3

subtract 9 from both sides then yes you can factor it out afterwards

Answer 4

K, thank you so much :)

Answer 5

Is this correct, it doesn't look like it is to me?

X^2 – 12x + 36 = 9
X^2 – 12x + 36 – 9 = 9 – 9
X^2 – 12x + 27
X^2 – 6 * x * 2 + 27
(x – 2)^2= 2

Answer 6

X^2 – 6 * x * 2 + 27
(x – 2)^2= 2

what did you do there?

Answer 7

Not sure what I was suppose to do, the instuctions from the instrutor said to find the square root of both sides. But I don't know how to find the square root of x

Answer 8

completing the square?? <---that is another method in finding x..what im doing is factoring

Answer 9

This is the example she gave us to go off of, she wants the problem done like this.

Given the quadratic function f(x) = x2 – 8x + 16, find a value of x such that f(x) = 4
Hint: First, the given function can be factored using perfect square trinomials, and then set the function equal to the value given for f(x). Look at example 5 on p. 706 for a similar example.
Answer: x = 6 and x = 2
Explanation:
Set x2 – 8x + 16 = 4 and factor x2 – 8x + 16 by using the rule for factoring perfect square trinomials to get:
(x – 4)2 = 4 Find the square root of both sides to get:
x – 4 = ± 2 Solve for x to get:
x = 4 + 2 = 6 and 4 – 2 = 2

Answer 10

lol why didnt you say so....it would be done IN THE BEGINNING...okay let's start again...

x^2 - 12x + 36 = 9

factor out x^2 - 12x + 36

Answer 11

Um, ok

Answer 12

That would be using the perfect square rule correct? That's what I followed when I facotered it out earlier

Answer 13

yup it is...and btw...x^2 - 12x + 27 isnt a perfect square trinomial that's why we couldnt do it there

Answer 14

K, so I would follow the same rules that I did earlier to get
x^2 - 12x - 36
(x - 2)^2 still following what the book says, which confuses me even more

Answer 15

(x-2)^2 = x^2 - 4x + 4!

(x-2)^2 is not a fixed for every thing that looks like this :p

Answer 16

I was just following the book and it skips around a lot :P
So after that step is when the square root comes in?

Answer 17

(x-2)^2 is not even right yet...let's factor out x^2 - 12x + 36 first

Answer 18

i assume you have an idea on factoring right?

Answer 19

Yeah, I just hate doing factoring so I always forget to do that part :)

Answer 20

rewrite x^2 - 12x + 36 as \[x^2 - 6x - 6x + 36\] now facot that

Answer 21

x^2 - 12x + 36
x^2=(x*x)
12x= (4*x*4)
36= (6*6)

Answer 22

-6x(x^2 +36)

Answer 23

what are you doing? hahaha :))) you factor by the one i stated \[x^2 - 6x - 6x + 36\]

Answer 24

That's how my brain works now, very frustrating :)

Answer 25

group it as \[(x^2 - 6x) + (-6x + 36)\] then factor out common factors

Answer 26

btw..6x(x^2 + 36) is equal to 6x^3 + 216x haha

Answer 27

That's what I hate about my brain I know that step but it passes it completely :)
(x^2 - 6x)+(-6x + 36)
-6x(x^2 + 36)
Then I believe you would factor out the x^2, at least that's what she had us do last class.

Answer 28

lol =)))) i now see what you're doing wrong! let me first ask you...do you know what "factor" means?

Answer 29

Used to mean to break the term down to prime numbers but my instructor doesn't like that. She showed us one way but for the tests we're expested to know exactly what she wants without telling us.

Answer 30

"factors" means terms that are multiplied...im talking about the basic-est math hehe

Answer 31

Ah ok, why couldn't she say that, it would make things so much easier :)
So after factoring the 36 to 6*6 I would take the steps I was jumping?

Answer 32

hmmm....let me do one step and maybe you can do the other....ill factor out x^2 - 6x watch what i do

(x)(x) <===that's x^2
(6)(x) <=== 6x

x^2 - 6x = (x)(x) - (6)(x)

now see how both of them have an x? that means i can "factor" out x

x(x - 6) <---factored form of x^2 - 6x

Answer 33

now do -6x + 36

Answer 34

-6x= 3x*2
36= 3*12
3x(2+12)

Answer 35

btw what i did was continuation of \((x^2 - 6x) + (-6x + 36)\) i simply factor out each "group"

Answer 36

Or would the x be with the 2, that part always throws me off

Answer 37

-6x = (-3)(x)(2)

36 = (3)(3)(2)(2)

^see how 36 doesnt have an x? therefore you cant factor out ..try again

Answer 38

therefore you cant factor out x is what i meant*

Answer 39

So it would be -3(2x + (3)(2)(2) or would the outside nuber be 3. The teacher never covered this in class at all and the example in the book don't show it

Answer 40

then ill be teaching you something new :P 2 is still common between the two...factor it out

Answer 41

So it's actually 2(3x + 3*3*2)

Answer 42

noooo!! 3 AND 2 are BOTH common

Answer 43

so I factor out both at the same time?

Answer 44

yes!

Answer 45

3*2(x+3*2), correct?

Answer 46

almost.... remember how -6x was NEGATIVE?

Answer 47

Crap I forgot that LOL. -3*2(x + 3*2)

Answer 48

hmmm...seems i need to teach you what happens in factoring....i'll use the first factor...x^2 - 6x

when i factored out x, this is what happened
\[\large x^2 - 6x = x(\frac{x^2}{x} - \frac{6x}{x}) =x(\frac{x^{\cancel{2}}}{\cancel{x}} - \frac{6\cancel{x}}{\cancel{x}}) = x(x - 6)\]

Answer 49

do you get my point?

Answer 50

yeah, that part I get. The part I don't get is factoring with only one negative number. I don't think you can make x a negative.

Answer 51

now what we did in -6x + 36...what did you factor out again?

Answer 52

I actored out the 3 and the 2

Answer 53

NEGATIVE 3 and 2 :P wwhich is also equal to -6 agree?

Answer 54

yeah

Answer 55

so \[-6x + 36 = -6(\frac{-6x}{-6} + \frac{36}{-6})\] what's the answer there?

Answer 56

-6(1x - 6)

Answer 57

Duh I see now :)

Answer 58

YAYY!!!

Answer 59

so the equation becomes \[x(x - 6) - 6(x - 6) = 9\] factor again

Answer 60

Would that be 3x(x+3) or is that completely screwed up, sorry I have a hard time going over thing that are new. Even if i just went over it :)

Answer 61

hmm think of (x-6) as a

ax - 6a..how would you factor that?

Answer 62

a(x-3*3) I think

Answer 63

a(x-6) is the right one :P now substitute a back

Answer 64

ax-6a if I multiply it

Answer 65

then you just went back to the original equation we had! i meant change a to (x-6) again...wasnt that what a meant?

Answer 66

OK, (x-6)(x-6)

Answer 67

GOOD! and that is...?

Answer 68

x^2 - 6x - 6x +36
x^2 +12x +36

Answer 69

do you notice that you just went back to what you had a while ago :P

Answer 70

I feel like such an idiot, I knew that :)

Answer 71

Hint: \(a \times a = a^2\)

Answer 72

So did that solve the problem or is there more to it?

Answer 73

what do you mean?

Answer 74

I thought there was a part that required square root or was it done already

Answer 75

i dont know what you're talking about :P haha you have \((x-6)(x-6)\) i am telling you that \(a \times a = a^2\)

Answer 76

Ok, I'm confused what does a*a=a^2 mean. I knew that much :)

Answer 77

it means that when you multiply two terms that are the same say \((x-6) \times (x-6)\) that is equal to \((x-6)^2\)

Answer 78

Haha, I knew that :D

Answer 79

so now we have \[(x-6)^2 = 9\] time to do your square root thing :PPP

Answer 80

Oh lord, I have never fully understood that part :)

Answer 81

you take the square root of both sides

Answer 82

Stupid question, how do you get the square root of a variable? I know the square root of 9 is 3

Answer 83

hmm let me ask this to you...what do you think is square root? what does it mean?

Answer 84

What times itself equals a number

Answer 85

Like 3*3=9

Answer 86

right! in other words what number when squared will result to that number correct?

Answer 87

yeah

Answer 88

square root of 9 means what number do you need to square to get 9...so what do you square to get (x-6)^2?

Answer 89

Hint: \(\sqrt{a^2} = a\)

Answer 90

would I make it x^2 - 36 before I find the square root? Sorry, my kids are trying to figure it out the wrong ways and confusing me in the process :)

Answer 91

noooo look at the hint i wrote...imagine x - 6 is a

Answer 92

\[\sqrt{a-6}^{2}=a + 36\] correct? or would it be different

Answer 93

nooo where did you get that 36?

Answer 94

and a....what?? that's x not a

Answer 95

LOL -6 * -6

Answer 96

why....why did you square it -_-

Answer 97

Told you I suck at this part :)

Answer 98

just look at the one i wrote square root of a^2 is a...now..what's square root of (x-6)^2??