Question

If AM = 8, AB = 16, and CD = 20, and if AM is shorter than CM, find CM.

So far I have:

Since AB = 16 and AM = 8 then MB must be 8 also

8 * 8 = x (20 - x )
64 = 20x - x²

Answer 1

no

Answer 2

No what?

Answer 3

am*mb = cm * md
8 * 8 = x * (20-x)

64 = 20x -x^2

x^2 -20x +64 = 0; we need to solve this quadratic equation

Answer 4

you did good up to there :)

Answer 5

we can "complete the square" by adding a useful form of zero.

see that -20x? we need half of it, and then square it to get a complete square out of this

Answer 6

minus the "x" par that is:

-20/2 = -10

(-10)^2 = 100; lets add 100 and subtract 100 from the equation

x^2 -20x+100 -100 +64 = 0

Answer 7

(x^2 -20x+100) -100 +64 = 0 ; now we can compact the square

(x -10)^2 -36 = 0

(x-10)^2 = 36

well, 6^2 = 36 so we should try that, but we have to +10 to get rid of the -10

x = 10 +- 6 will work

Answer 8

x = 10 + 6 = 10

x = 10 - 6 = 4 ; now we gotta determine which one they want :)

Answer 9

am < cm

8 < 16 or 4?

id go with 16; which would have been great if i hadnt typoed it upt here

Answer 10

16 is correct! :)

What are you.. a geometry genius?! :D

Answer 11

nah; its the algebra that does the work :)

Answer 12

Time to take the quiz!

* Runs in terror *

Answer 13

Yay! I passed my quiz :D

Thank you for your help! :)

Answer 14

TEST time -_-