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Find the value of x.​

Find the value of x.​-example-1
User Piohen
by
8.3k points

1 Answer

11 votes

Answer:

x = 5

Explanation:

Two secants have equal ratios when (in this case) they are split up as

AB * AC = AD*AE

Givens

AB = x-2

AC = (x - 2 + x+ 4) = 2x + 2

AD = 4

AE = 5 + 4 = 9

Substitute and solution

(x - 2) (2x + 2) = 4 (9) Expand the left, Combine the right

2(x^2 - x - 2) = 36 Divide both sides by 2

x^2 - x - 2 = 18 Subtract 18 from both sides

x^2 - x - 2 - 18 = 18 - 18 Combine

x^2 - x - 20 = 0 This factors

(x - 5)(x + 4) = 0 Only one of these factors works

x - 5 = 0 Add 5 to both sides.

x = 5

User Doug Finke
by
8.7k points

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