{"id":"cb_question_bank:3bbc7575-e2d2-4579-b41a-0c420a9db765","source_id":"cb_question_bank","source_item_id":"3bbc7575-e2d2-4579-b41a-0c420a9db765","external_id":null,"ibn":"08137-DC","question_id":"3de7a7d7","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":"E","score_band":2,"answer_type":"mcq","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"Which of the following is a solution to the equation 2 x squared, minus 4, equals x squared ?","stimulus":"","stimulus_html":null,"stem_html":"<p class=\"stem_paragraph \">Which of the following is a solution to the equation <span class=\"math_expression \"><span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/2832c3fe2071f19a3105911fe32522f6ec890c9815d19384ebe4028d689d557e\" alt=\"2 x squared, minus 4, equals x squared\"></span></span> ?</p>\n","rationale_html":"<p>Choice B is correct. Subtracting <span class=\"italic\">x</span><sup>2</sup> from both sides of the given equation yields <span class=\"italic\">x</span><sup>2</sup> – 4 = 0. Adding 4 to both sides of the equation gives <span class=\"italic\">x</span><sup>2</sup> = 4. Taking the square root of both sides of the equation gives <span class=\"italic\">x</span> = 2 or <span class=\"italic\">x</span> = –2. Therefore, <span class=\"italic\">x</span> = 2 is one solution to the original equation.</p><p class=\"tcp-9d8041ce-388a-4d17-b627-3a24b2379e05\">Alternative approach: Subtracting <span class=\"italic\">x</span><sup>2</sup> from both sides of the given equation yields <span class=\"italic\">x</span><sup>2</sup> – 4 = 0. Factoring this equation gives <span class=\"italic\">x</span><sup>2</sup> – 4 = (<span class=\"italic\">x</span> + 2)(<span class=\"italic\">x</span> – 2) = 0, such that <span class=\"italic\">x</span> = 2 or <span class=\"italic\">x</span> = –2. Therefore, <span class=\"italic\">x</span> = 2 is one solution to the original equation.</p><p>Choices A, C, and D are incorrect and may be the result of computation errors.</p><p></p>\n","correct_answer":["B"],"has_media":true,"has_mathml":false,"has_table":false,"source_created_at":"2023-08-02T20:25:59.634000+00:00","source_updated_at":"2023-08-02T20:25:59.634000+00:00","options":[{"label":"A","content_html":"<p>1</p>\n","ord":0},{"label":"B","content_html":"<p>2</p>\n","ord":1},{"label":"C","content_html":"<p>3</p>\n","ord":2},{"label":"D","content_html":"<p>4</p>\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}}