9
advanced-math

Solve: (2x+1)2=25(2x + 1)^2 = 25

A

x=2,−3x = 2, -3

B

x=3,−2x = 3, -2

C

x=12,−13x = 12, -13

D

x=2,3x = 2, 3

Correct Answer: A

Choice A is the correct answer.

  1. Take the square root: 2x+1=±52x + 1 = \pm 5.
  2. Set up two cases:
    • 2x+1=5⇒2x=4⇒x=22x + 1 = 5 \Rightarrow 2x = 4 \Rightarrow x = 2
    • 2x+1=−5⇒2x=−6⇒x=−32x + 1 = -5 \Rightarrow 2x = -6 \Rightarrow x = -3

Choice B is incorrect because of sign errors. Choice C is incorrect because it solved x+1=25/2x + 1 = 25/2 incorrectly. Choice D is incorrect because it misses the negative case properly.

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Set 3: Quadratic Equations and Functions 3