Solve For X please help, thank you :}

Question

asked Feb 18, 2022 43.7k views

1 Answer

Sanzy · Answer 1 · 2022-02-25T02:22:18+0000

Given:

Two secants intersecting each other outside the side the circle.

To find:

The value of x.

Solution:

Using Intersecting Secant Theorem, we get

x(x+8)=4(4+8)

x^2+8x=4(12)

x^2+8x=48

x^2+8x-48=0

Using splitting the middle terms, we get

x^2+12x-4x-48=0

x(x+12)-4(x+12)=0

(x+12)(x-4)=0

Using zero product property, we get

$(x+12)=0\text{ and }(x-4)=0$

$x=-12\text{ and }x=4$

Side length cannot be negative, i.e.,
$x\\eq -12$ .

Therefore, the only value of x is 4.