{"id":"cb_practice_pdf:t9-math-m2-q14","source_id":"cb_practice_pdf","source_item_id":"t9-math-m2-q14","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":2,"position":14,"stem":"z^2 +10z−24 = 0 What is one of the solutions to the given equation?","stimulus":"","stimulus_html":null,"stem_html":"<p>z^2 +10z−24 = 0 What is one of the solutions to the given equation?</p>","rationale_html":"<p>-12 The correct answer is either 2 or . The left-hand side of the given equation -24 10 can be rewritten by factoring. The two values that multiply to and add to 12 - are and 2. It follows that the given equation can be rewritten as +12 -2 =0 +12=0 ^z h^z h . Setting each factor equal to 0 yields two equations: z -2=0 12 +12=0 and z . Subtracting from both sides of the equation z results in =-12 -2=0 = z . Adding 2 to both sides of the equation z results in z 2. Note that 2 and -12 are examples of ways to enter a correct answer.</p>","correct_answer":["2"],"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}}