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# constructing equations/solve for x watch

1. Hey guys,
Im very frustrated I cannot see a method to answer this question correctly.
Any help is much appreciated.

'Two rectangles have the same are but different dimensions. The dimensions of the first are (2x + 2) by (x - 1) and the second are (x + 3) by (x + 1).
Find value of x and the area.'

I (think I) know what x equals but only by expanding and substituting until I found a number that satisfied the equality. ie. 2x^2 - 2 = x^2 - 4x + 3
(x = 5, area = 48). I know that this is not the way to go about it. Can anyone help with the correct method? I tried to differentiate but that didnt seem to get me anywhere.
2. Do you not know how to solve a quadratic equation? ._.
3. Your equality is incorrect it should say

(Original post by jdinsaanen)
2x^2 - 2 = x^2 + 4x + 3
From here you get

And that gives

Since x is not -1 it must be 5
4. (Original post by jdinsaanen)
Hey guys,
Im very frustrated I cannot see a method to answer this question correctly.
Any help is much appreciated.

'Two rectangles have the same are but different dimensions. The dimensions of the first are (2x + 2) by (x - 1) and the second are (x + 3) by (x + 1).
Find value of x and the area.'

I (think I) know what x equals but only by expanding and substituting until I found a number that satisfied the equality. ie. 2x^2 - 2 = x^2 - 4x + 3
(x = 5, area = 48). I know that this is not the way to go about it. Can anyone help with the correct method? I tried to differentiate but that didnt seem to get me anywhere.
Recap

Given

as long as

(if this is not true, then the roots aren't real, i.e they are complex).

However, in this case, you have sufficiently nice values of a and b to factorise the equation into the form

where m and n are such that

In order to do this, you look for two numbers (here, they are m and n) such that their sum is b and their product is c.

You are ONLY after the positive solution as lengths cannot be negative.
5. (Original post by TenOfThem)
From here you get

And that gives

Since x is not -1 it must be 5
Sorry, I just dont see how you got x^2 - 4x - 5

The rest I understand.
6. (Original post by Indeterminate)
Recap
Thank you for your feedback. I understand the uses of the discriminant but Im not getting answers for x that make any sense when I use the quadratic formula.
I know I missing something obvious but it just not coming to me.
7. (Original post by jdinsaanen)
Thank you for your feedback. I understand the uses of the discriminant but Im not getting answers for x that make any sense when I use the quadratic formula.
I know I missing something obvious but it just not coming to me.
Subtract

from both sides of the equation.
8. (Original post by Indeterminate)
Subtract

from both sides of the equation.
Many thanks for your help. Ive got it.

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