{"id":"cb_question_bank:367f1aeb-0542-4d83-bc41-1c178206156c","source_id":"cb_question_bank","source_item_id":"367f1aeb-0542-4d83-bc41-1c178206156c","external_id":"441e80ee-d059-4eb1-b33c-69ae14eabe0e","ibn":null,"question_id":"d0a53ef5","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":7,"answer_type":"spr","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"StartRoot left parenthesis x minus 2 right parenthesis squared EndRoot equals StartRoot 3 x plus 34 EndRoot What is the smallest solution to the given equation?","stimulus":"","stimulus_html":null,"stem_html":"

\n\t\n\t\t\n\t\t\t\n\t\t\t\t\n\t\t\t\t\tx\n\t\t\t\t\t-\n\t\t\t\t\t2\n\t\t\t\t\n\t\t\t\n\t\t\t2\n\t\t\n\t\n\t=\n\t\n\t\t\n\t\t\t\n\t\t\t\t3\n\t\t\t\tx\n\t\t\t\n\t\t\t+\n\t\t\t34\n\t\t\n\t\n\n

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What is the smallest solution to the given equation?

","rationale_html":"

The correct answer is -3. Squaring both sides of the given equation yields x-22=3x+34, which can be rewritten as x2-4x+4=3x+34. Subtracting \n\t3\n\tx\n\n and 34\n from both sides of this equation yields x2-7x-30=0. This quadratic equation can be rewritten as x-10x+3=0. According to the zero product property, x-10x+3 equals zero when either x-10=0 or x+3=0. Solving each of these equations for x\n yields x=10 or x=-3. Therefore, the given equation has two solutions, 10\n and -3\n. Of these two solutions, -3\n is the smallest solution to the given equation.

","correct_answer":["-3"],"has_media":false,"has_mathml":true,"has_table":false,"source_created_at":"2023-08-02T20:25:59.823000+00:00","source_updated_at":"2023-08-02T20:25:59.823000+00:00","options":[],"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}}