Question

http://www.sketchtoy.com/38641591
Would this one be what could be multiplied to get -20 but added to get -5? @jim_thompson5910

Answer 1

It's not going to be a whole number...you're going to have to use the quadratic formula

Answer 2

I'm factoring it. :P

Answer 3

if you cant factor it, and you've gone through all of the factor pairs for 20

you have to use the quadratic equation and/or complete the squares

Answer 4

-20

Answer 5

I have no clue what that is...

Answer 6

Which one...the formula or completing the square?

Answer 7

\[\frac{ -b \pm \sqrt{b^2 - 4ac} }{ 2a }\]

This is the quadratic formula

Answer 8

both...

Answer 9

The 'a' 'b' and 'c' represent your coefficients

a being the coefficient of your a² (which is 1)
b being the coefficient of your -5a (which is -5)
and
c being the coefficient of your -20 (which is just -20)

so you would replace every 'a' 'b' and 'c' in that equation...with the corresponding values

Answer 10

Can you set that up for me? >. <

Answer 11

Of course :) hang on

Answer 12

\[\frac{ 5 \pm \sqrt{(-5)^2 - 4(1)(-20)} }{ 2(1) }\]

Answer 13

so lets solve it....lets start what that giant square root thing

-5² = 25

25 - 4(1)(-20)

-4 times 1 = -4....-4 times -40 = 160

so we have

\[\frac{ 5 \pm \sqrt{25 + 160} }{ 2 }\]

Answer 14

now 25 + 160 = 185

so we have

\[\frac{ 5 \pm \sqrt{185} }{ 2 }\]

Answer 15

this sets up 2 equations

\[\frac{ 5 + \sqrt{185} }{ 2 }\]

and

\[\frac{ 5 - \sqrt{185} }{ 2 }\]

Answer 16

And when you solve these...you will have your 2 roots

Answer 17

I got something really weird for \[\sqrt{185}\]

Answer 18

Right...like I said, it's not going to be a whole number

√185 = 13.6014705087 right?

Answer 19

Yes.

Answer 20

okay so our 2 equations are going to be

\[\frac{ 5 + 13.6014705087 }{ 2 }\]

and

\[\frac{ 5 - 13.6014705087 }{ 2 }\]

Answer 21

Okay. > . < Do I divide that now:

Answer 22

Haha yes you must go through that wonderful process to get your roots :P

Answer 23

Divide it by the long number only orrr?

Answer 24

WAIT!!!! typo above lol

Answer 25

I bring you back to this post

"so lets solve it....lets start what that giant square root thing

-5² = 25

25 - 4(1)(-20)

-4 times 1 = -4....-4 times -40 = 160
"

-4 times 1 = -4....-4 times -40 = 160
this should be

-4 times 1 = -4....-4 times -20 = 80

Answer 26

so then we would have 25 + 80 = 105

Answer 27

so everything else is right....except our 2 equations are

\[\frac{ 5 + \sqrt{105} }{ 2 }\]

and

\[\frac{ 5 - \sqrt{105} }{ 2 }\]

Answer 28

*sorry about that*

Answer 29

It's fine. I got another really long number.

Answer 30

√105 = 10.2469507659. right?

Answer 31

yes

Answer 32

so lets solve these equations 1 by 1

\[\frac{ 5 + 10.2469507659 }{ 2 }\]

so you add 5 to that long number....then divide that by 2...what do you get...?

Answer 33

5.12347538295

Answer 34

Not quite what I get

5 + 10.2469507659 = 15.2469507659 right?

now what is THAT divided by 2?

Answer 35

That's what I got > . <

Answer 36

really?

15.2469507659
----------------
2

I get

7.62347538295

try checking it 1 more time :)

Answer 37

Oopsies, hehe c: I got your answer.

Answer 38

:) haha

okay so that would be 1 root....

the other...means we solve that other equation

\[\frac{ 5 - 10.2469507659 }{ 2 } = ?\]

Answer 39

so 5 - that giant number.....then that divided by 2 equals ...?

Answer 40

2.62347538295

Answer 41

missing something...

5 minus a number bigger than 5 = a negative number right?

so this should be

-2.62347538295 right?

Answer 42

Oops, yeah

Answer 43

So these are our 2 roots...if you want to see this in "factored form" it would look like

(a + 7.62347538295)(a - 2.62347538295)

Answer 44

And we can check to make sure it is correct

remember they have to add to make -5

and multiply to make -20

so

does -7.62347538295 + 2.62347538295 = -5?

and

does -7.62347538295 * 2.62347538295 = -20?

Answer 45

sorry again typo

"So these are our 2 roots...if you want to see this in "factored form" it would look like

(a + 7.62347538295)(a - 2.62347538295)
"

should be

(a - 7.62347538295)(a + 2.62347538295)

Answer 46

I hope that all made sense! :)

Answer 47

Made sense! Thanks for helping (: