{"id":"cb_question_bank:c5da11b9-22a3-4e19-9201-d97618f6f82a","source_id":"cb_question_bank","source_item_id":"c5da11b9-22a3-4e19-9201-d97618f6f82a","external_id":"5069a621-921f-40db-8e07-7253b4a9383b","ibn":null,"question_id":"ff2e5c76","program":"SAT","module":"math","domain_code":"P","domain":"Advanced Math","skill_code":"P.B.","skill":"Nonlinear equations in one variable and systems of equations in two variables","difficulty":"H","score_band":6,"answer_type":"mcq","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"x squared minus 40 x minus 10 equals 0 What is the sum of the solutions to the given equation?","stimulus":"","stimulus_html":null,"stem_html":"

\n\t\n\t\t\n\t\t\tx\n\t\t\t2\n\t\t\n\t\t-\n\t\t\n\t\t\t40\n\t\t\tx\n\t\t\n\t\t-\n\t\t10\n\t\n\t=\n\t0\n\n

\n

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

","rationale_html":"

Choice D is correct. Adding 10\n to each side of the given equation yields \n\t\n\t\t\n\t\t\tx\n\t\t\t2\n\t\t\n\t\t-\n\t\t\n\t\t\t40\n\t\t\tx\n\t\t\n\t\n\t=\n\t10\n\n. To complete the square, adding 4022, or 202, to each side of this equation yields x2-40x+202=10+202, or \n\t\n\t\t\n\t\t\t\n\t\t\t\tx\n\t\t\t\t-\n\t\t\t\t20\n\t\t\t\n\t\t\n\t\t2\n\t\n\t=\n\t410\n\n. Taking the square root of each side of this equation yields x-20=±410. Adding 20\n to each side of this equation yields x=20±410. Therefore, the solutions to the given equation are x=20+410 and x=20-410. The sum of these solutions is 20+410+20-410, or 40\n.

\n

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

\n

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

\n

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

","correct_answer":["D"],"has_media":false,"has_mathml":true,"has_table":false,"source_created_at":"2023-08-02T20:25:59.825000+00:00","source_updated_at":"2023-08-02T20:25:59.825000+00:00","options":[{"label":"A","content_html":"

0\n

","ord":0},{"label":"B","content_html":"

5\n

","ord":1},{"label":"C","content_html":"

10\n

","ord":2},{"label":"D","content_html":"

40\n

","ord":3}],"attribution":{"source_id":"cb_question_bank","source_name":"College Board digital SAT question bank (community dump)","rights_holder":"College Board","canonical_url":"https://satsuitequestionbank.collegeboard.org/","retrieved_from":"https://raw.githubusercontent.com/mdn522/sat-question-bank/main/data/cb-digital-questions.json","attribution":"SAT practice questions © College Board, from the official SAT Suite Question Bank. Retrieved via the community dump at github.com/mdn522/sat-question-bank.","disclaimer":"SAT® and PSAT/NMSQT® are trademarks registered by the College Board, which is not affiliated with, does not sponsor, and does not endorse this project.","license":"College Board copyright; source repository carries no licence. Local use only.","redistributable":false,"item_count":2017}}