Question

what value completes the square for the expression x^2+20x

Answer 1

What is the coefficient of x?

Answer 2

1?

Answer 3

The coefficient of x is the number in front of the x

Answer 4

20

Answer 5

Divide that number by 2

Answer 6

10

Answer 7

Square that number

Answer 8

100

Answer 9

That is the number that completes the square.

Answer 10

ok but whats the reasoning behind it

Answer 11

The reasoning is that all trinomials that are perfect square trinomials share this property:

one-half the coefficient of x, when squared, is the constant term.

Answer 12

Note these examples:

Answer 13

\[x^2+6x+9=(x+3)^2\]

Answer 14

Notice that the coefficient of x is 6. 1/2 of 6 is 3. 3^2 is 9

Answer 15

oh ok i understand now mind helping me out on a different problem?

Answer 16

\[x^2-2x+1=(x-1)^2\]
Notice that the coefficient of x is -2. 1/2 of -2 is -1 . (-1)^2=1

Answer 17

What is it?

Answer 18

Simplify the number using the imaginary unit i:

\[\sqrt{-496}\]

Answer 19

Do you know the definition of i?

Answer 20

do not but i know its used to remove the negative

Answer 21

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

Answer 22

\[\sqrt{-496}=\sqrt{16\times 31\times (-1)}=\sqrt{16}\sqrt{31}\sqrt{-1}=4\sqrt{31} i\]

Answer 23

ok i understand its just difficult for me to gett the two numbers that times to 496 etc

Answer 24

You could always write the prime factors.

Answer 25

what about square root of -240 and -169

Answer 26

240=4 x 60=4 x 4 x 15=16 x 15
169=13^2

Answer 27

alright thanks last one please

Answer 28

What is it?

Answer 29

24x2+3x

Answer 30

i dont know which 2 numbers add to 24 and multiply to 3

Answer 31

What are you supposed to do with that? Factor it?

Answer 32

yes factored form

Answer 33

There is a common factor of 3x. Factor it out

Answer 34

so its 3(8x+1)

Answer 35

Did you factor out 3x as instructed?

Answer 36

Is 3(8x+1)=24x^2+3x ?????

Answer 37

dude am lost

Answer 38

Why don't you just put 3x(8x+1) ?
I said to factor out 3x

Answer 39

so i did do it right

Answer 40

If you think that
\[3x(8x+1)\]
is the same as
\[3(8x+1)\]
then I suppose you could say you did it right but I would not say that.

Answer 41

ok i forgot x

Answer 42

what about simplifying expressions
(-2+9i)+(-7+3i) i got 33i-59

Answer 43

14-6i-63i+27^i^2=14-69i-27=-13-69i

Answer 44

What test are you taking anyway?

Answer 45

alg 2 midterm review your helping me out a lot and i forgot 14 i wrote 4 but i understand it

Answer 46

Good

Answer 47

what about -2+4i/3-i?

Answer 48

Multiply numerator and denominator by 3+i

Answer 49

so 6-i/9-i^2?

Answer 50

What is i^2?

Answer 51

The whole point is to get rid of the "i" in the denominator.

Answer 52

\[\frac{-2+4i}{3-i}\times \frac{3+i}{3+i}=\frac{-6-2i+12i+4i^2}{9-i^2}=\frac{-6+10i+4(-1)}{9-(-1)}=\frac{-10+10i}{10}=\]

Answer 53

\[-1+i\]

Answer 54

oh alright thanks man for everything

Answer 55

You had better learn to multiply binomials