document.write( "Question 179343: Can you please help me solve this radical equaqtion? \"sqrt%28x-1%29%2Bx=3\"
\n" ); document.write( "This problem did not come from a text book, it came from a worksheet.\r
\n" ); document.write( "\n" ); document.write( "I began by isolating the radical: \"sqrt%28x-1%29=-x%2B3\"
\n" ); document.write( "Then I squared each side to eliminate the radical: \"sqrt%28x-1%29%5E2=%28-x%2B3%29%5E2\"
\n" ); document.write( "Which gave me: \"+x-1=-x%5E2%2B9+\"
\n" ); document.write( "Then I moved everything to one side to give me a quadradtic equation:
\n" ); document.write( "\"x%5E2%2Bx-10=0\"
\n" ); document.write( "This is where I got stuck, I don't see how this can be factored, so I tried using the quadratic equation and just got confused from there. Can you help me please??!!???
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Algebra.Com's Answer #134251 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
Can you please help me solve this radical equaqtion? \"sqrt%28x-1%29%2Bx=3\"
\n" ); document.write( "This problem did not come from a text book, it came from a worksheet.\r
\n" ); document.write( "\n" ); document.write( "I began by isolating the radical: \"sqrt%28x-1%29=-x%2B3\"
\n" ); document.write( "Then I squared each side to eliminate the radical: \"sqrt%28x-1%29%5E2=%28-x%2B3%29%5E2\"
\n" ); document.write( "Which gave me: \"+x-1=-x%5E2%2B9+\"
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\r\n" );
document.write( "There's your error!\r\n" );
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document.write( "\"%28-x%2B3%29%5E2\" IS NOT \"-x%5E2%2B9\"!\r\n" );
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\r\n" );
document.write( "When there are two terms added to be squared, you must\r\n" );
document.write( "write it in parentheses TWICE and multiply it by itself, \r\n" );
document.write( "using FOIL. Also you must remember that when you square \r\n" );
document.write( "a negative, such as \"%28-x%29\" you get a positive \"%22%22%2Bx%5E2\",\r\n" );
document.write( "not \"-x%5E2\":\r\n" );
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document.write( "Therefore when you got to\r\n" );
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document.write( "\"sqrt%28x-1%29%5E2=%28-x%2B3%29%5E2\"\r\n" );
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document.write( "the next step should have been\r\n" );
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document.write( "\"x-1=%28-x%2B3%29%28-x%2B3%29\"\r\n" );
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document.write( "Then you must use \"FOIL\":\r\n" );
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document.write( "\"x-1=%28-x%29%28-x%29+%2B+%28-x%29%283%29+%2B+%283%29%28-x%29+%2B+%283%29%283%29\"\r\n" );
document.write( "\r\n" );
document.write( "\"matrix%281%2C3%2Cx-1%2C+%22=%22%2C%22%22%2Bx%5E2+-+3x+-+3x+%2B+9%29\"\r\n" );
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document.write( "You don't need to write that \"%22%22%2B%22%22\". I just\r\n" );
document.write( "put it there to remind you that when you square\r\n" );
document.write( "a negative you get a positive.\r\n" );
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document.write( "\"matrix%281%2C3%2Cx-1%2C%22=%22%2Cx%5E2-3x-3x%2B9%29\"\r\n" );
document.write( "\r\n" );
document.write( "\"x-1=x%5E2-6x%2B9\"\r\n" );
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document.write( "Then move everything right and you get:\r\n" );
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document.write( "\"0=x%5E2-7x%2B10\"\r\n" );
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document.write( "or if you like the 0 on the right, just swap sides:\r\n" );
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document.write( "\"x%5E2-7x%2B10=0\"\r\n" );
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document.write( "Then it factors nicely as\r\n" );
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document.write( "\"%28x-5%29%28x-2%29=0\"\r\n" );
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document.write( "Then you get the solutions \"x=5\" and \"x=2\"\r\n" );
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document.write( "But you must check these, because when you square\r\n" );
document.write( "both sides or multiply both sides by a variable,\r\n" );
document.write( "you may get extraneous solutions:\r\n" );
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document.write( "Checking \"x=5\"\r\n" );
document.write( "\"sqrt%28x-1%29%2Bx=3\"\r\n" );
document.write( "\"sqrt%285-1%29%2B5=3\"\r\n" );
document.write( "\"sqrt%284%29%2B5=3\"\r\n" );
document.write( "\"2%2B5=3\"\r\n" );
document.write( "\"7=3\"\r\n" );
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document.write( "That doesn't check, so \"x=5\" is not a \r\n" );
document.write( "genuine solution, but is called \"extraneous\".\r\n" );
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document.write( "Checking \"x=2\"\r\n" );
document.write( "\"sqrt%28x-1%29%2Bx=3\"\r\n" );
document.write( "\"sqrt%282-1%29%2B2=3\"\r\n" );
document.write( "\"sqrt%281%29%2B2=3\"\r\n" );
document.write( "\"1%2B2=3\"\r\n" );
document.write( "\"3=3\"\r\n" );
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document.write( "That checks. So \"x=2\" is the only solution\r\n" );
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document.write( "Edwin
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