Answered

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Answer:  C) 4

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Work Shown:

Applying the tangent-secant theorem will allow us to solve for x

x*(x+5) = (x+2)^2

x^2+5x = (x+2)*(x+2)

x^2+5x = x^2+4x+4

5x = 4x + 4 ..... subtracting x^2 from both sides; terms cancel

5x-4x = 4

x = 4

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Check:

Plug in x = 4

x*(x+5) = (x+2)^2

4*(4+5) = (4+2)^2

4*(9) = (6)^2

36 = 36

The answer is confirmed.

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