Question

http://prntscr.com/bywr41

Can you give me an example problem so I can learn how to do this one?

Answer 1

Have you learned the quadratic formula?

Answer 2

If I did, I don't remember it.

Answer 3

quadratic formula
\[\Large x = \frac{-b\pm\sqrt{b^2-4ac}}{2a}\]

Answer 4

hopefully that looks familiar?

Answer 5

Oh, then no I have not, I took Pre-Algebra last year.

Answer 6

ok there's another way but it doesn't work for all quadratics

Answer 7

it will work for this case though

Answer 8

are you able to factor out the GCF?

Answer 9

Oh, uh. Could you teach me how?

Answer 10

what factor do you see in 5, 60 and 180? what's common in all three?

Answer 11

5.

Answer 12

divide each term by 5

5/5 = 1
60/5 = 12
180/5 = 36

so we would go from
5x^2 + 60x + 180
to
5*(1x^2 + 12x + 36)

Answer 13

you can distribute the 5 back in to get 5x^2 + 60x + 180 back again

Answer 14

Hang on, let me get something to write on.

Answer 15

I'm ready to learn. :)

Answer 16

do you see how I went from
5x^2 + 60x + 180
to
5*(1x^2 + 12x + 36)
??

Answer 17

I'm not quite understanding how you turned 5x^2 into 5*(1x^2)?

Answer 18

I divided 5 by itself

5/5 = 1

Answer 19

I also divided the other terms by 5 too

50/5 = 12
180/5 = 36

Answer 20

So why would the (5*) be there?

Answer 21

60/5 = 12 I mean

Answer 22

so that you can distribute the 5 back in to get the original expression again

Answer 23

Oh okay, I get it.

Answer 24

it's like 2*(7x+5) = 2*7x + 2*5 = 14x+10

Answer 25

Mhm, yeah, distributive property.

Answer 26

thinking backwards
14x/2 = 7x
10/2 = 5

so 14x+10 = 2*(7x+5)

Answer 27

1x^2 + 12x + 36 is the same as x^2 + 12x + 36

to factor x^2 + 12x + 36 you need to think of numbers that multiply to 36 and add to 12

Answer 28

Perhaps 4?

Answer 29

4 and what else?

Answer 30

Oh okay okay.

Let's see...

2, 4, and 6?

Answer 31

let's list out all the ways to multiply to 36

1*36
2*18
3*12
4*9
6*6


which pair of factors will add to 12?

Answer 32

it's not 1 and 36 since 1+36 = 37

Answer 33

Oh, you asked what numbers to multiply, okay, got it.

Answer 34

2*6
3*4
12*1?

Answer 35

let's list out all the ways to multiply to 36

1*36
2*18
3*12
4*9
6*6


which pair of factors will \(\Large \text{add}\) to 12?

Something like 2 and 18 will not work. Yes they multiply to 36
2*18 = 36
but they do NOT add to 12 since 2+18 = 20

Answer 36

I'm thinking 6*6

Answer 37

yes
6*6 = 36
6+6 = 12

Answer 38

so x^2+12x+36 factors to (x+6)(x+6)

Answer 39

5x^2+60x+180 = 5*(x^2+12x+36) = 5*(x+6)*(x+6)


So
5x^2+60x+180 = 0
will turn into
5*(x+6)*(x+6) = 0

Answer 40

what comes next?

Answer 41

I assume you multiply, or use distributive property.

Answer 42

hint: If A*B = 0, then either A = 0 or B = 0

Answer 43

example: (x+2)*(x+5) = 0 means either x+2 = 0 or x+5 = 0

Answer 44

I'm not quite getting it.

Answer 45

if you had 2*x = 0, then what must x be?

Answer 46

0.

Answer 47

if you had x*y = 0, then either x is zero or y is zero. Agreed?

Answer 48

Yes.

Answer 49

is it possible that x is not zero and y is not zero and have x*y = 0 still?

Answer 50

Oh, no.

Answer 51

One of the two terms might be a different number.

Answer 52

This rule is known as the zero product property

Answer 53

zero product property:
if x*y = 0, then either x = 0 or y = 0 (or both could be zero)

Answer 54

so we have (x+6)*(x+6) = 0

which means either x+6 = 0 or x+6 = 0

which boils down to just x+6 = 0

Answer 55

if x+6 = 0 then x = ???

Answer 56

-6?

Answer 57

yes, so that wraps up the problem

if 5x^2 + 60x + 180 = 0, then x = -6

Answer 58

what happens when you replace every x in 5x^2 + 60x + 180 with -6?

Answer 59

Lemme write it down, uno momento.

Answer 60

un momento

Answer 61

and ok

Answer 62

I'm confused. 5x^2 = 5(-6)^2, as if -6 were to equal x?

Answer 63

And then (-30)^2, which is 900 right?

Answer 64

it's not just 5x^2

it's 5x^2 + 60x + 180

Answer 65

Well, I'm aware of that, I was just trying to input x into that first part there.

Answer 66

also 5(-6)^2 does not equal (-30)^2

you are using PEMDAS wrong

Answer 67

exponents come before multiplication

Answer 68

OH, I need PEMDAS, haha. Okay, one moment.

Answer 69

So (-6)^2 would be the first thing I do in that first part?

Answer 70

yes

Answer 71

Is this right? http://prntscr.com/byx3r5

Answer 72

on the line where you have 5(-6)^2, I would have 60(-6)+180 = 0 added on as well

Answer 73

here's how I'd do it

5x^2 + 60x + 180 = 0

5(-6)^2 + 60(-6) + 180 = 0

5(36) + 60(-6) + 180 = 0

180 - 360 + 180 = 0

-180 + 180 = 0

0 = 0

Answer 74

I ended up doing that in a later step, but still got the right answer.

Answer 75

so that's how you would check to see if you got the right answer or not.

Answer 76

Thank you for so much for your help, I didn't mean to take up so much time. :P

Answer 77

that's ok. I'm glad I could help