Question

Rhett decides to build a square room for his movie and music collection. If the area of the room is 9x2 − 6x + 1 square feet, what is the length of one side of the room?

Answer 1

a side would be square root of the area, no?\[\sqrt{9x^2-6x+1}\]

Answer 2

idk thats why I'm asking for help haha

Answer 3

\[side \times side = area\] for a square.
so the side of this square is \[\sqrt{9x^2−6x+1}\]----------------------------------------------------------------

to do this, we have to factor 9x^2 -6x + 1
compare\[9x^2 - 6x + 1 \text{ with } a^2 - 2ab + b^2\]can you tell me what a is and what b is?

Answer 4

a should be 9 i believe and 6 is b? not sure

Answer 5

no no o:
\[(3x)^2 = 9x^2 \text{ so a should be 3x}\]\[(-1)^2 = 1 \text{ so b should be -1}\]\[\text{ then -2ab will be -6x}\]thennnnnn
\[a^2 - 2ab +b^2 = (a-b)^2\]\[9x^2-6x+1 = (? - ?)^2\]

Answer 6

what are you asking me to do?

Answer 7

figure out those "?" ~ (? - ?) is the answer

Answer 8

3x-1?

Answer 9

ya, do you understand how we got that?

Answer 10

yes. you square root the original problem to get one of the sides

Answer 11

yup, all right

Answer 12

thanks!