constructing equations/solve for x

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.

Reply 1

aznkid66

1

Do you not know how to solve a quadratic equation? ._.

Reply 2

TenOfThem

18

Your equality is incorrect it should say

Original post by jdinsaanen

2x^2 - 2 = x^2 + 4x + 3

From here you get

x^2 - 4x - 5

And that gives

(x+1)(x-5)

Since x is not -1 it must be 5

Reply 3

Indeterminate

3

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

ax^2 + bx + c =0

x=\dfrac{-b \pm \sqrt{b^2 - 4ac }}{2a}

as long as

b^2 \geq 4ac

(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

(x-m)(x-n)=0

where m and n are such that

am^2 + bm + c =0

an^2 + bn + c=0

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.

(edited 11 years ago)

Reply 4

jdinsaanen

OP

Original post by TenOfThem

From here you get

x^2 - 4x - 5

And that gives

(x+1)(x-5)

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.

Reply 5

jdinsaanen

OP

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.

Reply 6

Indeterminate

3

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.