145,609 views
7 votes
7 votes
Can anyone help find x for both problems? It would be appreciated!​

Can anyone help find x for both problems? It would be appreciated!​-example-1
User Kyle Campos
by
3.2k points

1 Answer

23 votes
23 votes

Answer:

Explanation:

What this formula says is that the external segment of the secant * the secant's entire length = the tangent squared

16

(x+2)^2 = 18(18 + 14) Add what is inside the brackets

(x +2)^2 = 18 * 32 Combine the right

(x + 2)^2 = 576 Take the square root of both sides

√(x + 2)^2 = √576

x + 2 = 24 Subtract 2 from both sides

x = 24 - 2

x = 22

I don't think you can use the minus value here.

14

Two secant theorem

The two secant theorem has both the left and right set up as having brackets.

8(19 + 8) = (x + 4)(3x + x+4) Simplify the right and left

8(27) = (x + 4)(4x + 4) Remove the right and left brackets

216 = 4(x + 4)( x + 1) Expand the right

216 = 4 (x^2 + 5x + 4) Divide both sides by 4

54 = x^2 + 5x + 4 Subtract 54 from both sides

x^2 + 5x - 50 Combine the left

x^2 + 5x - 50 = 0 Factor

(x + 10)(x - 5) = 0

I think the only usable factor is x - 5 = 0

x = 5

User TheRealMrCrowley
by
3.3k points