{"id":117,"date":"2026-01-12T15:48:49","date_gmt":"2026-01-12T15:48:49","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/qrpracticepages\/?post_type=chapter&p=117"},"modified":"2026-01-12T15:48:49","modified_gmt":"2026-01-12T15:48:49","slug":"non-linear-equations-get-stronger-answer-key","status":"publish","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/qrpracticepages\/chapter\/non-linear-equations-get-stronger-answer-key\/","title":{"raw":"Non-Linear Equations Get Stronger Answer Key","rendered":"Non-Linear Equations Get Stronger Answer Key"},"content":{"raw":"

Quadratic Equations<\/span><\/h2>\r\n
    \r\n \t
  1. [latex]x=6[\/latex], [latex]x=3[\/latex]<\/li>\r\n \t
  2. [latex]x=-\\dfrac{5}{2}[\/latex], [latex]x=-\\dfrac{1}{3}[\/latex]<\/li>\r\n \t
  3. [latex]x=5[\/latex], [latex]x=-5[\/latex]<\/li>\r\n \t
  4. [latex]x=-\\dfrac{3}{2}[\/latex], [latex]x=\\dfrac{3}{2}[\/latex]<\/li>\r\n \t
  5. [latex]x=-2[\/latex], [latex]x=3[\/latex]<\/li>\r\n \t
  6. [latex]x=0[\/latex], [latex]x=-\\dfrac{3}{7}[\/latex]<\/li>\r\n \t
  7. [latex]x=-6[\/latex], [latex]x=6[\/latex]<\/li>\r\n \t
  8. [latex]x=6[\/latex], [latex]x=-4[\/latex]<\/li>\r\n \t
  9. [latex]x=1[\/latex], [latex]x=-2[\/latex]<\/li>\r\n \t
  10. [latex]x=-2[\/latex], [latex]x=11[\/latex]<\/li>\r\n \t
  11. [latex]x=3\\pm\\sqrt{22}[\/latex]<\/li>\r\n \t
  12. [latex]z=\\dfrac{2}{3}[\/latex], [latex]z=-\\dfrac{1}{2}[\/latex]<\/li>\r\n \t
  13. [latex]x=\\dfrac{3+\\sqrt{17}}{4}[\/latex]<\/li>\r\n \t
  14. Not real<\/li>\r\n \t
  15. One rational<\/li>\r\n \t
  16. Two real; rational<\/li>\r\n \t
  17. [latex]x=\\dfrac{-1\\pm\\sqrt{17}}{2}[\/latex]<\/li>\r\n \t
  18. [latex]x=\\dfrac{5\\pm\\sqrt{13}}{6}[\/latex]<\/li>\r\n \t
  19. [latex]x=\\dfrac{-1\\pm\\sqrt{17}}{8}[\/latex]<\/li>\r\n \t
  20. [latex](x+\\frac{b}{2a})^2=\\dfrac{b^2-4ac}{4a^2}[\/latex]\r\n[latex]x+\\dfrac{b}{2a}=\\pm\\sqrt{\\dfrac{b^2-4ac}{4a^2}}[\/latex]\r\n[latex]x=\\dfrac{-b\\pm\\sqrt{b^2-4ac}}{2a}[\/latex]<\/li>\r\n \t
  21. [latex]x(x+10)=119[\/latex]; [latex]7[\/latex] ft. and [latex]17[\/latex] ft.<\/li>\r\n \t
  22. maximum at [latex]x=70[\/latex]<\/li>\r\n \t
  23. The quadratic equation would be [latex](100x-0,5x^2)-(60x+300)=300[\/latex]. The two values of [latex]x[\/latex] are [latex]20[\/latex] and [latex]60[\/latex].<\/li>\r\n \t
  24. [latex]3[\/latex] feet<\/li>\r\n<\/ol>\r\n

    Other Types of Equations<\/span><\/h2>\r\n
      \r\n \t
    1. [latex]x\\neq-4[\/latex]; [latex]x=-3[\/latex]<\/li>\r\n \t
    2. [latex]x\\neq1[\/latex]; when we solve this we get [latex]x=1[\/latex], which is excluded, therefore NO solution<\/li>\r\n \t
    3. [latex]x\\neq0[\/latex]; [latex]x=-\\dfrac{5}{2}[\/latex]<\/li>\r\n \t
    4. [latex]x=81[\/latex]<\/li>\r\n \t
    5. [latex]x=17[\/latex]<\/li>\r\n \t
    6. [latex]x=8[\/latex], [latex]x=27[\/latex]<\/li>\r\n \t
    7. [latex]x=-2,1,-1[\/latex]<\/li>\r\n \t
    8. [latex]y=0,\\dfrac{3}{2},-\\dfrac{3}{2}[\/latex]<\/li>\r\n \t
    9. [latex]m=1,-1[\/latex]<\/li>\r\n \t
    10. [latex]x=\\dfrac{2}{5},\\pm3i[\/latex]<\/li>\r\n \t
    11. [latex]x=32[\/latex]<\/li>\r\n \t
    12. [latex]t=\\dfrac{44}{3}[\/latex]<\/li>\r\n \t
    13. [latex]x=3[\/latex]<\/li>\r\n \t
    14. [latex]x=-2[\/latex]<\/li>\r\n \t
    15. [latex]x=4,-\\dfrac{4}{3}[\/latex]<\/li>\r\n \t
    16. [latex]x=-\\dfrac{5}{4},\\dfrac{7}{4}[\/latex]<\/li>\r\n \t
    17. [latex]x=3,-2[\/latex]<\/li>\r\n \t
    18. [latex]x=-5[\/latex]<\/li>\r\n \t
    19. <\/li>\r\n \t
    20. [latex]10[\/latex] in.<\/li>\r\n \t
    21. <\/li>\r\n \t
    22. [latex]90[\/latex] kg<\/li>\r\n \t
    23. [latex](-\\infty,\\infty)[\/latex]<\/li>\r\n \t
    24. [latex](-\\infty,-\\dfrac{10}{3})\\cup(4,\\infty)[\/latex]<\/li>\r\n \t
    25. [latex](-\\infty,-4]\\cup[8,+\\infty)[\/latex]<\/li>\r\n \t
    26. No solution<\/li>\r\n \t
    27. [latex](-5,11)[\/latex]<\/li>\r\n<\/ol>","rendered":"

      Quadratic Equations<\/span><\/h2>\n
        \n
      1. [latex]x=6[\/latex], [latex]x=3[\/latex]<\/li>\n
      2. [latex]x=-\\dfrac{5}{2}[\/latex], [latex]x=-\\dfrac{1}{3}[\/latex]<\/li>\n
      3. [latex]x=5[\/latex], [latex]x=-5[\/latex]<\/li>\n
      4. [latex]x=-\\dfrac{3}{2}[\/latex], [latex]x=\\dfrac{3}{2}[\/latex]<\/li>\n
      5. [latex]x=-2[\/latex], [latex]x=3[\/latex]<\/li>\n
      6. [latex]x=0[\/latex], [latex]x=-\\dfrac{3}{7}[\/latex]<\/li>\n
      7. [latex]x=-6[\/latex], [latex]x=6[\/latex]<\/li>\n
      8. [latex]x=6[\/latex], [latex]x=-4[\/latex]<\/li>\n
      9. [latex]x=1[\/latex], [latex]x=-2[\/latex]<\/li>\n
      10. [latex]x=-2[\/latex], [latex]x=11[\/latex]<\/li>\n
      11. [latex]x=3\\pm\\sqrt{22}[\/latex]<\/li>\n
      12. [latex]z=\\dfrac{2}{3}[\/latex], [latex]z=-\\dfrac{1}{2}[\/latex]<\/li>\n
      13. [latex]x=\\dfrac{3+\\sqrt{17}}{4}[\/latex]<\/li>\n
      14. Not real<\/li>\n
      15. One rational<\/li>\n
      16. Two real; rational<\/li>\n
      17. [latex]x=\\dfrac{-1\\pm\\sqrt{17}}{2}[\/latex]<\/li>\n
      18. [latex]x=\\dfrac{5\\pm\\sqrt{13}}{6}[\/latex]<\/li>\n
      19. [latex]x=\\dfrac{-1\\pm\\sqrt{17}}{8}[\/latex]<\/li>\n
      20. [latex](x+\\frac{b}{2a})^2=\\dfrac{b^2-4ac}{4a^2}[\/latex]
        \n[latex]x+\\dfrac{b}{2a}=\\pm\\sqrt{\\dfrac{b^2-4ac}{4a^2}}[\/latex]
        \n[latex]x=\\dfrac{-b\\pm\\sqrt{b^2-4ac}}{2a}[\/latex]<\/li>\n
      21. [latex]x(x+10)=119[\/latex]; [latex]7[\/latex] ft. and [latex]17[\/latex] ft.<\/li>\n
      22. maximum at [latex]x=70[\/latex]<\/li>\n
      23. The quadratic equation would be [latex](100x-0,5x^2)-(60x+300)=300[\/latex]. The two values of [latex]x[\/latex] are [latex]20[\/latex] and [latex]60[\/latex].<\/li>\n
      24. [latex]3[\/latex] feet<\/li>\n<\/ol>\n

        Other Types of Equations<\/span><\/h2>\n
          \n
        1. [latex]x\\neq-4[\/latex]; [latex]x=-3[\/latex]<\/li>\n
        2. [latex]x\\neq1[\/latex]; when we solve this we get [latex]x=1[\/latex], which is excluded, therefore NO solution<\/li>\n
        3. [latex]x\\neq0[\/latex]; [latex]x=-\\dfrac{5}{2}[\/latex]<\/li>\n
        4. [latex]x=81[\/latex]<\/li>\n
        5. [latex]x=17[\/latex]<\/li>\n
        6. [latex]x=8[\/latex], [latex]x=27[\/latex]<\/li>\n
        7. [latex]x=-2,1,-1[\/latex]<\/li>\n
        8. [latex]y=0,\\dfrac{3}{2},-\\dfrac{3}{2}[\/latex]<\/li>\n
        9. [latex]m=1,-1[\/latex]<\/li>\n
        10. [latex]x=\\dfrac{2}{5},\\pm3i[\/latex]<\/li>\n
        11. [latex]x=32[\/latex]<\/li>\n
        12. [latex]t=\\dfrac{44}{3}[\/latex]<\/li>\n
        13. [latex]x=3[\/latex]<\/li>\n
        14. [latex]x=-2[\/latex]<\/li>\n
        15. [latex]x=4,-\\dfrac{4}{3}[\/latex]<\/li>\n
        16. [latex]x=-\\dfrac{5}{4},\\dfrac{7}{4}[\/latex]<\/li>\n
        17. [latex]x=3,-2[\/latex]<\/li>\n
        18. [latex]x=-5[\/latex]<\/li>\n
        19. <\/li>\n
        20. [latex]10[\/latex] in.<\/li>\n
        21. <\/li>\n
        22. [latex]90[\/latex] kg<\/li>\n
        23. [latex](-\\infty,\\infty)[\/latex]<\/li>\n
        24. [latex](-\\infty,-\\dfrac{10}{3})\\cup(4,\\infty)[\/latex]<\/li>\n
        25. [latex](-\\infty,-4]\\cup[8,+\\infty)[\/latex]<\/li>\n
        26. No solution<\/li>\n
        27. [latex](-5,11)[\/latex]<\/li>\n<\/ol>\n","protected":false},"author":15,"menu_order":4,"template":"","meta":{"_candela_citation":"[]","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"part":106,"module-header":"- Select Header -","content_attributions":[],"internal_book_links":[],"video_content":null,"cc_video_embed_content":{"cc_scripts":"","media_targets":[]},"try_it_collection":null,"_links":{"self":[{"href":"https:\/\/content.one.lumenlearning.com\/qrpracticepages\/wp-json\/pressbooks\/v2\/chapters\/117"}],"collection":[{"href":"https:\/\/content.one.lumenlearning.com\/qrpracticepages\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/content.one.lumenlearning.com\/qrpracticepages\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/qrpracticepages\/wp-json\/wp\/v2\/users\/15"}],"version-history":[{"count":1,"href":"https:\/\/content.one.lumenlearning.com\/qrpracticepages\/wp-json\/pressbooks\/v2\/chapters\/117\/revisions"}],"predecessor-version":[{"id":125,"href":"https:\/\/content.one.lumenlearning.com\/qrpracticepages\/wp-json\/pressbooks\/v2\/chapters\/117\/revisions\/125"}],"part":[{"href":"https:\/\/content.one.lumenlearning.com\/qrpracticepages\/wp-json\/pressbooks\/v2\/parts\/106"}],"metadata":[{"href":"https:\/\/content.one.lumenlearning.com\/qrpracticepages\/wp-json\/pressbooks\/v2\/chapters\/117\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/content.one.lumenlearning.com\/qrpracticepages\/wp-json\/wp\/v2\/media?parent=117"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/qrpracticepages\/wp-json\/pressbooks\/v2\/chapter-type?post=117"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/qrpracticepages\/wp-json\/wp\/v2\/contributor?post=117"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/qrpracticepages\/wp-json\/wp\/v2\/license?post=117"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}