What is the value of x?

i know the answer is 2 but i need a explanation as to how to get that

When 2 secants intersect a circle:
(DC + CE) * CE = (AB + BE) * BE

( 1 + (x+4)) * (x+4) = (11 + (x+1)) * (x+1)

x + x^2 + 4x + 4 +4x +16 = 11x +x^2 +x +11 +x +1

9x + 20 = 13x + 12

4x = 8

x = 2

Source:
http://www.1728.org/circangl.htm
Scroll down to Two Intersecting Secants

Gee - that was a little bit of work!!

When 2 secants intersect a circle:
(DC + CE) * CE = (AB + BE) * BE

( 1 + (x+4)) * (x+4) = (11 + (x+1)) * (x+1)

x + x^2 + 4x + 4 +4x +16 = 11x +x^2 +x +11 +x +1

9x + 20 = 13x + 12

4x = 8

x = 2

Source:
http://www.1728.org/circangl.htm
Scroll down to Two Intersecting Secants

Gee - that was a little bit of work!!

Use the information to write the dimensions of each rectangle in terms of w, the width of the 1st one.

1st rectangle;
l = 2w
w = 2

2nd rectangle:
w = w 
l = 2w + 4

If the area of the 2nd rectangle is 70 square meters, you will use the area formula to write an equation that you will solve using the factoring.

A = lw
70 = w(2w + 4)
70 = 2w^2 + 4w
0 = 2w^2 + 4w -70
0 = 2 (w^2 +2w - 35)
0 = 2 (w + 7) (w - 5)

To get zero, the width would need to be -7 or 5.  Because it is a distance, it has to be 5 meters.

The width of both rectangles is 5 meters.