{"id":"cb_practice_pdf:t9-math-m1-q21","source_id":"cb_practice_pdf","source_item_id":"t9-math-m1-q21","external_id":null,"ibn":null,"question_id":null,"program":"SAT","module":"math","domain_code":null,"domain":null,"skill_code":null,"skill":null,"difficulty":null,"score_band":null,"answer_type":"spr","answer_source":"rationale","layout_warning":null,"form_id":"cb_practice_pdf:test-9","module_number":1,"position":21,"stem":"(x−2)^2 = 3x+34 What is the smallest solution to the given equation?","stimulus":"","stimulus_html":null,"stem_html":"<p>(x−2)^2 = 3x+34 What is the smallest solution to the given equation?</p>","rationale_html":"<p>- The correct answer is 3. Squaring both sides of the given equation yields -2 2=3 +34 2-4 +4=3 +34 ^x h x , which can be rewritten as x x x . Subtracting 3x 34 2-7 -30=0 and from both sides of this equation yields x x . This quadratic -10 +3 =0 equation can be rewritten as ^x h^x h . According to the zero product -10 +3 -10=0 +3=0 property, ^x h^x h equals zero when either x or x . Solving =10 =- each of these equations for x yields x or x 3. Therefore, the given 10 - - equation has two solutions, and 3. Of these two solutions, 3 is the smallest solution to the given equation.</p>","correct_answer":["3"],"has_media":false,"has_mathml":false,"has_table":false,"source_created_at":null,"source_updated_at":null,"options":[],"attribution":{"source_id":"cb_practice_pdf","source_name":"College Board full-length SAT practice tests (PDF)","rights_holder":"College Board","canonical_url":"https://satsuite.collegeboard.org/practice/practice-tests/paper","retrieved_from":"https://satsuite.collegeboard.org/practice/practice-tests/paper","attribution":"Full-length SAT practice tests 4–11 © College Board, published free at satsuite.collegeboard.org.","disclaimer":"Extracted from PDF layout: equations, figures and tables do not survive intact. Use the original PDFs for anything the text renders poorly. SAT® is a trademark registered by the College Board, which is not affiliated with and does not endorse this project.","license":"College Board copyright. Free to download; not licensed for redistribution.","redistributable":false,"item_count":905}}