Question #ff2e5c76 - SAT Suite Question Bank

ID: ff2e5c76

Modded SAT Question Bank by Abdullah Mallik

$x^{2} - 40 x - 10 = 0$

What is the sum of the solutions to the given equation?

$0$
$5$
$10$
$40$

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Correct Answer: D

Rationale

Choice D is correct. Adding $10$ to each side of the given equation yields $x^{2} - 40 x = 10$ . To complete the square, adding $left parenthesis StartFraction 40 Over 2 EndFraction right parenthesis squared$ , or $20 squared$ , to each side of this equation yields $x^{2} - 40 x + 20^{2} = 10 + 20^{2}$ , or ${(x - 20)}^{2} = 410$ . Taking the square root of each side of this equation yields $x - 20 = \pm \sqrt{410}$ . Adding $20$ to each side of this equation yields $x = 20 \pm \sqrt{410}$ . Therefore, the solutions to the given equation are $x = 20 + \sqrt{410}$ and $x = 20 - \sqrt{410}$ . The sum of these solutions is $(20 + \sqrt{410}) + (20 - \sqrt{410})$ , or $40$ .

Choice A is incorrect and may result from conceptual or calculation errors.

Choice B is incorrect and may result from conceptual or calculation errors.

Choice C is incorrect and may result from conceptual or calculation errors.

Question Difficulty: Hard