Question

x-16x+64=81

Answer 1

x-16x simplifies to _____

Answer 2

(x-8)^2?

Answer 3

oh is there a square in there?

Answer 4

is the first x supposed to be squared?

Answer 5

yes it's x^2-16x+64=81

Answer 6

oh ok

Answer 7

so yes, the left side factors to (x-8)^2

Answer 8

x^2-16x+64=81

turns into

(x-8)^2 = 81

Answer 9

then you take the square root of both sides (don't forget the plus/minus) to get

x-8 = sqrt(81) or x-8 = -sqrt(81)

what's next?

Answer 10

x=89,x=-77?

Answer 11

sqrt(81) = 9

Answer 12

so

x-8 = sqrt(81) or x-8 = -sqrt(81)

then turns into

x-8 = 9 or x-8 = -9

Answer 13

so i have to square root the answer first then solve?

Answer 14

correct

Answer 15

so x=17, x=-1?

Answer 16

?

Answer 17

yep, you got it

Answer 18

k what about this problem.... x^2-18x+81=100...big numbers are intimidating to me

Answer 19

would it be (x-9)^2

Answer 20

so you would get (x-9)^2 = 100

Answer 21

take the square root of both sides

Answer 22

so does it look like x-9=sqrt100
>>x-9=10>> x-9=-10
x=-19,
x=-1?

Answer 23

\[x-9 = \pm 10\]

Answer 24

x-9 = 10

x = 10+9

x = 19 is your first solution

Answer 25

x = -1 is the second, so you got that part right

Answer 26

ok thanks ...x^2+4x+_?=(x+_?)^2

Answer 27

take half of 4 and square it to fill in the first blank

Answer 28

the second blank is just half of the x coefficient

Answer 29

show me?

Answer 30

what's half of 4

Answer 31

2

Answer 32

square that to get ____

Answer 33

4

Answer 34

now what

Answer 35

so that goes in the first blank

Answer 36

the second blank is 2 because that's half of 4 (the x coefficient)

Answer 37

k got it and 4 in the next ?

Answer 38

2 in the next

Answer 39

because (x+2)^2 = x^2 + 4x + 4

Answer 40

oh ok gotcha!

Answer 41

what if the equation becomes negative such as x^2-4x+_?=(x-_?)^2 is this like the difference of squares

Answer 42

half of -4 is ____

Answer 43

-2

Answer 44

square that to get ____

Answer 45

4

Answer 46

so that goes in the first blank

Answer 47

now you just factor x^2 - 4x + 4 to find the value that goes in the second blank

Answer 48

ok great complete the square problem:

x^2+4x+3=0

Answer 49

last one...

take half of 4 to get 2

then square it to get 4

add this to both sides to get

x^2 + 4x + 3 + 4 = 4

x^2 + 4x + 4 + 3 = 4

(x^2 + 4x + 4) + 3 = 4

(x+2)^2 + 3 = 4

(x+2)^2 = 4-3

(x+2)^2 = 1

I'll let you finish up

Answer 50

where did the 4's go though is it subtracted?
on the other side

Answer 51

what do you mean