I am trying to solve a problem and get down to
w2+5w-4w-20=0 they simplified it to
w(w+5)-4(w+5) cant figure out how the first came to the second equation

Question

I am trying to solve a problem and get down to 
w2+5w-4w-20=0   they simplified it to 
w(w+5)-4(w+5)  cant figure out how the first came to the second equation

HeartTricker · Answer

Hi, what exactly are we doing here?

parikhst · Answer

well the full question is "a rectangles length is 2 units more than twice its width.  its area is 40 square units.  the equation  w(2w+2)=40 can be used to find w, the width of the rectangle   what is the width

snowflake0531 · Answer

The distributive property says $a(b+c) = a(b) + a(c)$ and $a(b-c) = a(b) - a(c)$

From ^ I think you can see how you came from the first equation to the second

snowflake0531 · Answer

@parikhst wrote:

well the full question is "a rectangles length is 2 units more than twice its width. its area is 40 square units. the equation w(2w+2)=40 can be used to find w, the width of the rectangle what is the width

So you have $w(2w+2)=40$ You can distribute the parenthesis and get $2w^2+2w=40$ then get it to one side of the equation $2w^2+2w-40$ It's better to simplify it before finding the roots (your answer) so you can do $2(w^2+w-20)$

parikhst · Answer

okay i get it to that point

snowflake0531 · Answer

From there, you can simplify it from $2(w^2+w-20)$ to $2(w+5)(w-4)$

snowflake0531 · Answer

Which makes your answer either -5 or 4
But since lengths can't be negative, it must be 4

parikhst · Answer

okay so the 2 just disapears?

snowflake0531 · Answer

Well, it's $2(w-4)(w+5)=0$ and as you should know $ab=c\a=c\b=c$

So, yeah, we just get rid of the 2

parikhst · Answer

gotch ya  okay i think that helps!

parikhst · Answer

thanks a lot everyone

snowflake0531 · Answer

yw~

parikhst · Answer

i also have one more question "a rectangle's width is one-fourth of its length. its area is 9 square units. the equation (1/4)*L=9 can be used to find L (length). what is length

parikhst · Answer

i thought it would be L=36

snowflake0531 · Answer

Well, the equation is actually $$L(\frac{1}{4}L)=9$$

parikhst · Answer

ohhh that would help!!! so u square root it duh

parikhst · Answer

didn't see the other L

snowflake0531 · Answer

square root it-?

parikhst · Answer

like L= square root of 36

snowflake0531 · Answer

ohhh yeah I'm slow

parikhst · Answer

nono its ok.  maybe i need my eyes checked

parikhst · Answer

thanks!

snowflake0531 · Answer

yw~