Can you show me the steps needed to be taking to get the answers?

Question

Not asking for answers per say, just help getting the answers. Don't tell me to do my own homework because I did. I'm just double checking to make sure I followed the steps correctly.

http://img159.imageshack.us/img159/7733/01cl8.png

Answer 1

If you have worked on these already, it would help to see your work to point out places where you are approaching the problem correctly or not. This would also give us confidence that you weren't just asking for us to do most of the work for you but had actually worked on these already.

Our only choice is to either give you the answers, give you all the work, or give you some hints to have you try them on your own. In this case, I'll go with this last method and hope you can double-check your own work.

1) (x-2) (2x - 5) = 0
This is already factored. The equation will be zero when either of the parts is zero. So solve for:
(x - 2) = 0 or (2x - 5) = 0
You should get two answers.

2) x² + 6x - 27 = 0
Start by factoring this as (x - 3)(x + 9) then use the same method as #1.

3) x² + 6 = -5x
Move everything to one side by adding 5x to both sides. One side will have 0. Then do the same as in #2 and #1.

4) 5x² = 2x - 7x²
Get everything on one side leaving 0 on the other. Note you will have a common factor of 2x you can factor out.

5) 3x² + 6x = 2x² - 9
Same as #4. Don't forget to combine like terms. It will end up being a perfect square. (One answer).

6) 5x² - 11x + 2 = 0
This is harder to factor. If you get lost use the quadratic formula. But you should be able to get:
(5x + 1)(x + 2) = 0

7) x² - 9 = 0
This factors as (x + 3)(x - 3) because it is a difference of squares. You could also make this x² = 9, but don't forget that -3 is a square root of 9.

8) Let w = width
Let w + 2 = length
Area = w(w + 2) = 24
Expand this out and get everything on one side. Solve like before, but just ignore the answer that is negative. The positive value will be the width, and the length is 2 more than that.

Answer 2

1.
(x-2)(2x-5)=0
x = 2 and x = 5/2

2.
x^2+6x-27=0
x^2+9x - 3x-27=0
x(x+9)-3(x+9)=0
(x+9)(x-3)=0
x=-9 and x = 3

3.
x^2+6=-5x
x^2+5x+6=0
x^2 + 3x + 2x + 6 = 0
x(x+3)+2(x+3)=0
(x+3)(x+2)=0
x = -3 and x = -2

4.
5x^2 = 2x - 7x^2
12x^2 - 2x = 0
2x(6x-2)=0
x = 0 and x = 1/3

5.
3x^2+6x=2x^2-9
x^2+6x+9=0
x^2+3x+3x+9=0
x(x+3)+3(x+3)=0
(x+3)(x+3)=0
x=-3

6.
5x^2 - 11x + 2 =0
5x^2 -10x - x + 2 = 0
5x(x-2)-1(x-2)=0
(5x-1)(x-2)=0
x=1/5 and x=2

7.
x^2 - 9 = 0
(x+3)(x-3)=0
x=-3 and x=3

8.
x(x+2)=24
x^2+ 2x -24 = 0
x^2 + 6x - 4x - 24 = 0
x(x+6)-4(x+6)=0
(x-4)(x+6)=0
x=4 or x = -6
since length cannot be negative, so x = 4

length of rectangle = 6, breadth of rectangle = 4

Answer 3

Just plug your answers into the
equation to see if it comes out right.
I will tell you that every problem except
5 and 8 have two distinct solutions.