Question

What are the possible values of x if the distance between the points (x, 8) and (–5, 3) is units?

{–2, 9}
{9, 1}
{–9, –1}
{–8, –3}

Answer 1

if the distance between the two points is radical41units

Answer 2

do you know the distance formula to find the distance between 2 points?

Answer 3

Here it is
http://www.purplemath.com/modules/distform.htm

Answer 4

the first step is write down the distance formula. can you do that?

Answer 5

yes i've done that

Answer 6

second step is substitute (x,8) for (x1,y1) in the formula, and (-5,3) for (x2,y2) in the formula
what do you get?

Answer 7

\[d=\sqrt{(-5-x)^2 + (3-8)^2}\]

Answer 8

good. also replace d with sqrt(41)

now square both sides.

Answer 9

1680=(-5-x) + (3-8) ?

Answer 10

lost the bubble.
first 41^2= 41*41= 1681 (not 1680)

however, the equation you start with is
\[ \sqrt{41}= \sqrt{ (-5-x)^2+ (3-8)^2} \]
if we square both sides, what do we get

note: sqrt(41)*sqrt(41) is not 1681.

Answer 11

41=(-5-x) + (3-8)

Answer 12

left side looks good. but try again on the right side
when you multiply
sqrt(a)*sqrt(a) you get a

if a is something complicated, it does not matter. the only thing that changes is that the sqrt sign goes away.

Answer 13

confused about the left side :/

Answer 14

you mean the right side?

sqrt(a+b+3)*sqrt(a+b+3) = a+b+3
sqrt(x^2/7)*sqrt(x^2/7) = x^2/7
sqrt( x^2 + y^2)* sqrt(x^2 + y^2) = x^2+y^2

do you see the pattern. what do you get with
sqrt( (-5-x)^2 + (3-8)^2)*sqrt( (-5-x)^2 + (3-8)^2)=

Answer 15

sorry i did mean the right. and i see the pattern. and would you get (-5-x)^2 + ( 3-8)^2 ?

Answer 16

yes, so now we have
41= (-5-x)^2 + (3-8)^2

next step. simplify (3-8)^2

Answer 17

25?

Answer 18

you should get (3-8)= -5 and -5*-5 = 25

now expand (-5-x)^2 :
(-5-x)*(-5-x) use FOIL to multiply this out

Answer 19

x^2+10x+25

Answer 20

so the equation is now
41= x^2+10x+25 + 25
can you simplify and solve for x?

Answer 21

wait how come there is an extra 25?

Answer 22

never mind. i got it

Answer 23

Your question is the reason it is always good to write down the original equation in its entirety, and as you simplify parts of it, rewrite the whole thing. otherwise you might leave something out.

Answer 24

i got stuck at -9=x^2+10x

Answer 25

add 9 to both sides to get
-9+9= x^2+10x+9
or
x^2+10x+9=0

can you factor this?

Answer 26

one way is list the factors of 9
1,9
3,3

do any of the pairs add to 10? yes the first pair
so (x+1)(x+9)=0
now find the 2 x values that make this 0

Answer 27

(x+3)(x+3)= x^2+6x+9 close, but no cigar

Answer 28

no cigar ? o.o

Answer 29

Just an expression...
when you have time, this video on factoring is useful
http://www.khanacademy.org/math/algebra/polynomials/v/factoring-quadratic-expressions

meanwhile, the answer here is
(x+1)(x+9)=0
this means either (x+1)=0 or (x+9)+0
the first equation x+1=0 becomes x=-1 and the 2nd gives us x= -9
so -1 and -9 are the answers.

Answer 30

see
http://www.phrases.org.uk/meanings/close-but-no-cigar.html

Answer 31

alright. thank you