Question

What is the value of X? (Please help, used 50 points!)

Answer 1

Answer: X=7

Explanation:

To Solve this problem we have to remember a formula regarding secants in circles it states (A+B)*B=(C+D)*D, I have attached said Theorem. This is Exactly what your problem is asking.

So First

B = 4

A = 10

D = x

C = 1

(A+B)*B=(C+D)*D

(10+4)*4=(1+x)*x

14*4=x²+x

-x²-x+56=0

Using Quadratic Formula

X = 7, X = -8

Since you cant have - side length X= -8 is Extraneous

Thus Final solution is X = 7

Answer 2

x=7

(x)(x+1)=(4)(4+10)

Explanation:

Expanding the right-hand side of the equation, we get:

(x)(x+1) = (4)(14)

Simplifying, we get:

x^2 + x = 56

Moving all terms to the left-hand side, we get:

x^2 + x - 56 = 0

Now we can factor this quadratic equation:

(x + 8)(x - 7) = 0

So the solutions are x = -8 or x = 7.