{"id":"cb_practice_pdf:t4-math-m2-q12","source_id":"cb_practice_pdf","source_item_id":"t4-math-m2-q12","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":"mcq","answer_source":"rationale","layout_warning":null,"form_id":"cb_practice_pdf:test-4","module_number":2,"position":12,"stem":"- −4x^2 −7x = −36 What is the positive solution to the given equation?","stimulus":"","stimulus_html":null,"stem_html":"<p>- −4x^2 −7x = −36 What is the positive solution to the given equation?</p>","rationale_html":"<p>- Choice B is correct. Multiplying each side of the given equation by 16 yields 2 + = 64 112x 576x. To complete the square, adding 49 to each side of this 2 + + = + ( )+2 = equation yields 64 112x 49 x576 49, or 8x 7 625. Taking the + = square root of each side of this equation yields two equations: 8x 7 25 and + =- + = 8x 7 25. Subtracting 7 from each side of the equation 8x 7 25 yields = =18 =9 8x 18. Dividing each side of this equation by 8 yields x , or x . 8 4 9 Therefore, is a solution to the given equation. Subtracting 7 from each side of 4 + =- =- the equation 8x 7 25 yields 8x 32. Dividing each side of this equation =- 9 - by 8 yields x 4. Therefore, the given equation has two solutions, and 4. 4 9 9 Since is positive, it follows that is the positive solution to the given equation. 4 4 2 Alternate approach: Adding 4x and 7x to each side of the given equation =2 + - yields 0 4 7x 36x. The right-hand side of this equation can be rewritten as 2 + - - 4 x16 9x 3x6. Factoring out the common factor of 4x from the first two - terms of this expression and the common factor of 9 from the second two ( + )- ( + ) ( + ) terms yields x4 x 4 9x 4. Factoring out the common factor of x 4 ( -)( +) from these two terms yields the expression 4 x9 x4. Since this expression - = + = is equal to 0, it follows that either x4 9 0 oxr 4 0. Adding 9 to each side - = = of the equation x4 9 0 yieldxs 4 9. Dividing each side of this equation by 4 =9 9 yields x . Therefore, is a positive solution to the given equation. Subtracting 4 4 + = =- 4 from each side of the equatioxn 4 0 yields x 4. Therefore, the given 9 - 9 9 equation has two solutions, and 4. Since is positive, it follows that is the 4 4 4 positive solution to the given equation. 7 Choice A is incorrect. Substituting for x in the given equation yields 4 -49=- 36, which is false. Choice C is incorrect. Substituting 4 for x in the given 2 - =- equation yields 92 36, which is false. Choice D is incorrect. Substituting 7 - =- for x in the given equation yields 245 36, which is false. 47 SAT PRACTICE TEST #4 ANSWER EXPLANATIONS SAT ANSWER EXPLANATIONS nnnnn MATH: MODULE 2</p>","correct_answer":["B"],"has_media":false,"has_mathml":false,"has_table":false,"source_created_at":null,"source_updated_at":null,"options":[{"label":"A","content_html":"<p>7/4</p>","ord":0},{"label":"B","content_html":"<p>9/4</p>","ord":1},{"label":"C","content_html":"<p>4</p>","ord":2},{"label":"D","content_html":"<p>7 -</p>","ord":3}],"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}}