Question

o

Answer 1

Is 64 a perfect square?

Answer 2

Is x^2 a square?

Answer 3

is it \[x^2 + 64?\]

Answer 4

What is the definition of a perfect square?

Answer 5

Hmm I say we teach her
If she gets it, medal is yours
I'm not here for the medal
i'm here to get her to understand the question :)

Answer 6

takes the square 8 time 8 is 64

Answer 7

How do you get x^2 in the first place?
What two variables do you multiply to get it?

Answer 8

Good! And what two numbers do you multiply to get 64? Obviously 8 right thanks to AA
What do these two have in common
x^2, 8^2

Answer 9

Good! Taking the square out. You get (x+8)^2
Expanding this: (x+8)^2.....
Will that give you x^2 + 64?

Answer 10

Actually it would not (x+8)^2 gives you x^2 + 16x + 64
What does that tell you about factoring x^2 + 64?

Answer 11

It tells you it cannot be factored
It is simply impossible
Every time you have something like x^2 + P where P is perfect square
You cannot factor it.
Does that make sense?

Answer 12

There are no factors with real numbers.

If you want complex number answer then (x + 8i)(x - 8i)

Answer 13

^That is exactly what the answer should be if you're doing a test

Answer 14

x^2 +64 = 0
And we get P(x)=x^2 +64
Now, we can look for the roots of P(x) using various Algorithm :

Solve by Factorization

x^2 +64 = 0
Separate : ( x^2 -8*i*x ) + ( 8*i*x +64 ) = 0
Commutative Law : ( x^2 8*i*x ) + ( -8*i*x +64 ) = 0
Distributive Law : x*( x 8*i ) + -8*i*( x 8*i ) = 0
Factor : ( x -8*i )*( x 8*i )

So the Polynomial have 2 roots :
x1 = 8*i
x2 = -8*i

Answer 15

You're right
There is no answer for that

Answer 16

How about x^2 - 64
Do you think this is factorable?

Answer 17

Look again. What changed from x^2 + 64 and x^2 - 64?

Answer 18

Yep. And so that means there is a possibility that this is factorable. Going back to where we left off with the other one...
we had (x+8). Putting a square outside would not make x^2 - 64

Answer 19

What two combinations make a negative? Think + and - and multiplication

Answer 20

Actually it doesn't matter which has the higher value in multiplication
But you're right
So to get x^2 - 64
What would you have to multiply (x+8) with?

Answer 21

do you have to multiply it by (x+8) again or (x-8)?

Answer 22

to check your answer
Expand (x+8)(x-8)
that should give you x^2 - 64

Answer 23

Notice how when you're combining like terms, there seems to be some cancelling out during expansion

Answer 24

The negative stuff was just a lesson you might learn later on
For now, you want to stick with showing that you cannot factor the two expressions
Show your work like AA showed his

Answer 25

Do you know the value of i?

Answer 26

nope i actually is
\[i = \sqrt{x^{-1}}\]

Answer 27

Can you square root that?

Answer 28

use the FOIL method to remember how to multiply two binomials (a+b)(c+d) First: a*c Outer a*d Inner: b*c Last: b*d now add up to get ac+ad+bc+bd if you have (a+b)(c -d) treat it like (a+b)(c+ -d) and do the same thing First: a*c Outer: a*-d Inner: b*c Last: b* -d put it all together: ac -ad +bc -bd

Answer 29

OOOPS so \[\ i = sqrt{-1}\]

Answer 30

\[i = \sqrt{-1}\]

Answer 31

just apply the (a+b)^2 formula (a+b)^2=a^2+b^2+2ab then you will get it....

Answer 32

after appling the formula you will see i^2 replace i^2 with -1 becouse "i" means imaginary number... i^2=-1

Answer 33

Lol don't say that
i equals to what i said up there
if you square i, what is its value?

Answer 34

Yep! So go back to your question and solve it using this knowledge

Answer 35

(x+9i)2
i is -1
as said by @OrthodoxMan

Answer 36

is it (x + 9i)2 or (x + 9i)^2?

Answer 37

the second one^
Let's see if she solves it
Pretty sure she is done

Answer 38

yep shes done i guess

Answer 39

Apply the square to the i as well

Answer 40

Remember what i^2 = ...

Answer 41

NO DONT GIVE UP
LOOL
Treat i as a variable
Substitute -1 into i
Hence you must do x^2 + 18(-1)

Answer 42

WHAT ON EARTH IS THIS?

Answer 43

MOVE AWAY BHUMI
WE BANISH YOU

Answer 44

that was pretty rude...oh well

Answer 45

Because you're smart
You need to keep practising
In no time, you'll be better than us

Answer 46

If you stop complaining and let me help you
I can go to sleep :P

Answer 47

lol sleep then i can try to help

Answer 48

Haha alright
thanks man
Make sure she finishes all of her questions

Answer 49

yep i will

Answer 50

oh,well shes offline -.-

Answer 51

-.- guess we can both get off
goodnight