2020 AMC 10A Problem 5

Below is the video solution and professionally curated solution for Problem 5 of the 2020 AMC 10A, from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2020 AMC 10A solutions, or check the answer key.

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Concepts:absolute value quadratic

Difficulty rating: 1020

What is the sum of all real numbers $x$ for which $|x^2-12x+34|=2?$

$12$

$15$

$18$

$21$

$25$

Video solution:

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Written solution:

The equation means $x^2-12x+34=2$ or $x^2-12x+34=-2$ . The first gives $x^2-12x+32=0$ , with roots $4$ and $8$ . The second gives $(x-6)^2=0$ , with root $6$ . The sum of all real solutions is $4+8+6=18$ . Thus, C is the correct answer.

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