6

Set 13: Quadratic Equations

Explanation

Answer: A

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

A.

x=2,3x = 2, -3

✓ Correct
B.

x=3,2x = 3, -2

C.

x=12,13x = 12, -13

D.

x=2,3x = 2, 3

Detailed Explanation

Choice A is correct. Choice A is the correct answer. 1. Take the square root: 2x+1=±52x + 1 = \pm 5. 2. Set up two cases: * 2x+1=52x=4x=22x + 1 = 5 \Rightarrow 2 x = 4 \Rightarrow x = 2 * 2x+1=52x=6x=32x + 1 = -5 \Rightarrow 2 x = -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.

Key Steps:

The correct answer is x=2,3x = 2, -3

Why others are wrong:
B: Choice B is incorrect and may result from a calculation error.
C: Choice C is incorrect and may result from a calculation error.
D: Choice D is incorrect and may result from a calculation error.

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