3

Set 11: Quadratic Equations

Explanation

Answer: A

(x−5)2=36(x - 5)^2 = 36. Solve.

A.

x=11x = 11 or x=−1x = -1

✓ Correct
B.

x=6x = 6 or x=−6x = -6

C.

x=41x = 41 or x=−31x = -31

D.

x=1x = 1 or x=−11x = -11

Detailed Explanation

Choice A is correct. Choice A is the correct answer. Take square root: x−5=±6x - 5 = \pm 6. So x=5+6=11x = 5 + 6 = 11 or x=5−6=−1x = 5 - 6 = -1. Verify: (11−5)2=36(11 - 5)^2 = 36 ✓ and (−1−5)2=36(-1 - 5)^2 = 36 ✓. Choice B is incorrect because these are the values of (x−5)(x - 5), not xx itself. Choice C is incorrect because these would solve (x−5)2=1296(x - 5)^2 = 1296 (wrong constant). Choice D is incorrect because the values and signs don't satisfy the equation.

Key Steps:

•

The correct answer is x=11x = 11 or x=−1x = -1

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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