document.write( "Question 30998: square root of 3x-5 minus square root x+7 equals 2 \n" ); document.write( "
Algebra.Com's Answer #17719 by AnlytcPhil(1806) $\"\"$ $\"About$
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square root of 3x-5 minus square root x+7 equals 2\r\n" );
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document.write( "                   Ö3x-5 - Öx+7 = 2\r\n" );
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document.write( "Isolate the radical term Ö3x-5 by adding Öx+7 to both sides. \r\n" );
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document.write( "                          Ö3x-5 = 2 + Öx+7 \r\n" );
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document.write( "Square both sides:\r\n" );
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document.write( "                          ____          ___\r\n" );
document.write( "                       (Ö3x-5)² = (2 + Öx+7)² \r\n" );
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document.write( "Careful here.  Since there is only ONE term in the parenthese on the left to be\r\n" );
document.write( "squared, and since it is a square root, we can just take away the radical and\r\n" );
document.write( "get 3x-5. But the right side id not so easy because there are TWO terms in the\r\n" );
document.write( "parentheses.  We must write the parenbtheses on the right with TWO terms twice\r\n" );
document.write( "and multiply using FOIL\r\n" );
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document.write( "                                        ___       ___\r\n" );
document.write( "                           3x-5 = (2 + Öx+7)(2 + Öx+7)\r\n" );
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document.write( "To use FOIL on the right we have\r\n" );
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document.write( "F = 2×2 = 4\r\n" );
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document.write( "O = 2Öx+7\r\n" );
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document.write( "I = 2Öx+7\r\n" );
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document.write( "L = (Öx+7)² = x+7\r\n" );
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document.write( "So we have\r\n" );
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document.write( "                           3x - 5 = F + O + I + L\r\n" );
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document.write( "                           3x - 5 = 4 + 2Öx+7 + 2Öx+7 + x + 7     \r\n" );
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document.write( "                           3x - 5 = 11 + 4Öx+7 + x\r\n" );
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document.write( "We again isolate the radical term 4Öx+7\r\n" );
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document.write( "                           2x - 16 = 4Öx+7\r\n" );
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document.write( "Evewry term can be divided by 2\r\n" );
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document.write( "                             x - 8 = 2Öx+7\r\n" );
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document.write( "Square both sides:\r\n" );
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document.write( "                          (x - 8)² = (2Öx + 7)²\r\n" );
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document.write( "                    (x - 8)(x - 8) = 2²(Öx + 7)²\r\n" );
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document.write( "                 x² - 8x - 8x + 64 = 4(x + 7)\r\n" );
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document.write( "                     x² - 16x + 64 = 4x + 28\r\n" );
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document.write( "                     x² - 20x + 36 = 0\r\n" );
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document.write( "                   (x - 18)(x - 2) = 0 \r\n" );
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document.write( "                   Answers: x = 18, x =2.\r\n" );
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document.write( "But we must ceck these in the original, because they both might be solutions,\r\n" );
document.write( "one might be a solution and the other not, or there may be no solutions at all.\r\n" );
document.write( "We substitute in the original equation:\r\n" );
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document.write( "                      Ö3x-5 - Öx+7 = 2  \r\n" );
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document.write( "                   _______    ____\r\n" );
document.write( "                  Ö3(18)-5 - Ö18+7 = 2\r\n" );
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document.write( "                         Ö49 - Ö25 = 2\r\n" );
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document.write( "                             7 - 5 = 2\r\n" );
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document.write( "                                 2 = 2    \r\n" );
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document.write( "This checks so x = 18 is a solution\r\n" );
document.write( "                       ____    ___\r\n" );
document.write( "                      Ö3x-5 - Öx+7 = 2  \r\n" );
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document.write( "                     ______    ____\r\n" );
document.write( "                    Ö3(2)-5 - Ö2+7 = 2\r\n" );
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document.write( "                           Ö1 - Ö9 = 2\r\n" );
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document.write( "                             1 - 3 = 2\r\n" );
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document.write( "                                -2 = 2\r\n" );
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document.write( "This does not check so x = 2 is NOT a solution                              \r\n" );
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document.write( "Edwin\r\n" );
document.write( "AnlytcPhil@aol.com
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