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# Solving quadratic equation

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1. My question was; "A rectangle has sides of length x+3cm and 3x-2cm, given that the area of the rectangle is 104cm^2, find the value of x"

I started out by doing the formula A=L x W and done x+3(3x-2) and by the end got
12x^2-8x= 104 then I made in a quadratic by making it 12x^2-8x-104= .

I am very stuck so I am pretty certain I have made a mistake, would any one be able to find my mistake and explain the process, thank you!!
2. (Original post by miaofcourse)
My question was; "A rectangle has sides of length x+3cm and 3x-2cm, given that the area of the rectangle is 104cm^2, find the value of x"

I started out by doing the formula A=L x W and done x+3(3x-2) and by the end got
12x^2-8x= 104 then I made in a quadratic by making it 12x^2-8x-104= .

I am very stuck so I am pretty certain I have made a mistake, would any one be able to find my mistake and explain the process, thank you!!
Your expansion is wrong:

Do you know that ?
3. (Original post by miaofcourse)
My question was; "A rectangle has sides of length x+3cm and 3x-2cm, given that the area of the rectangle is 104cm^2, find the value of x"

I started out by doing the formula A=L x W and done x+3(3x-2) and by the end got
12x^2-8x= 104 then I made in a quadratic by making it 12x^2-8x-104= .

I am very stuck so I am pretty certain I have made a mistake, would any one be able to find my mistake and explain the process, thank you!!
4. (Original post by Zacken)
Your expansion is wrong:

Do you know that ?
Thank you!! I see it now, in my working out I thought it was x+3x not x+3 haha
5. (Original post by miaofcourse)
Thank you!! I see it now, in my working out I thought it was x+3x not x+3 haha
Ahhh, glad it's sorted now!
6. (Original post by Zacken)
Ahhh, glad it's sorted now!
so to simplify it would be 3x^2+7x-6 and then in brackets (3x+2)(x-3) how would that become the value of x?
7. (Original post by miaofcourse)
so to simplify it would be 3x^2+7x-6 and then in brackets (3x+2)(x-3) how would that become the value of x?
When either bracket = 0 the whole thing = 0
and we know x>0
8. (Original post by miaofcourse)
so to simplify it would be 3x^2+7x-6 and then in brackets (3x+2)(x-3) how would that become the value of x?
Hey! That's not correct.

You started with then make it to get and now solve this by factorising or using the quadratic formula.
9. (Original post by Zacken)
Hey! That's not correct.

You started with then make it to get and now solve this by factorising or using the quadratic formula.
So it become (3x+22)(x-5) then x=-22 and x=5 and as after it says to work out the lenth and a length cannot be negative then x is 5?!
10. (Original post by miaofcourse)
So it become (3x+22)(x-5) then x=-22 and x=5 and as after it says to work out the lenth and a length cannot be negative then x is 5?!
looks right
11. (Original post by miaofcourse)
So it become (3x+22)(x-5) then x=-22 and x=5 and as after it says to work out the lenth and a length cannot be negative then x is 5?!
Plug it back through the rectangle lengths to check.

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