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?

Question

anonymous · Answer

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

anonymous · Answer

idk thats why I'm asking for help haha

anonymous · Answer

$$side \times side = area$$ 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?

anonymous · Answer

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

anonymous · Answer

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
$$a^2 - 2ab +b^2 = (a-b)^2$$$$9x^2-6x+1 = (? - ?)^2$$

anonymous · Answer

what are you asking me to do?

anonymous · Answer

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

anonymous · Answer

3x-1?

anonymous · Answer

ya, do you understand how we got that?

anonymous · Answer

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

anonymous · Answer

yup, all right

anonymous · Answer

thanks!