Question

Find the value of x.

Answer 1

Answer:

Step-by-step explanation:

Comment

The square of the tangent = the external segment of the secant * the full length of the secant.

Formula

(x - 1)^2 = (x - 3)*(x - 3 + 5)                   Combine the right

Solution

(x - 1)^2 = (x - 3)*(x +2)                         Remove the brackets on both sides

x^2 - 2x + 1 = x^2 -3x + 2x - 6            Combine the right

x^2 - 2x + 1 = x^2 - x - 6                     Subtract x^2 from both sides

-2x + 1 = - x - 6                                    Add 6 to both sides

-2x + 1 + 6 = -x - 6 + 6                         Combine

-2x + 7 = - x                                         Add 2x to both sides

-2x+2x + 7 = -x+2x                              Combine

7 = x

Answer

x = 7