document.write( "Question 416819: x = √ (16x + 225) \n" ); document.write( "
Algebra.Com's Answer #291925 by Edwin McCravy(20055) $\"\"$ $\"About$
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document.write( "     _________\r\n" );
document.write( "x = √16x + 225\r\n" );
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document.write( "Square both sides\r\n" );
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document.write( "x² = (√16x + 225)²\r\n" );
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document.write( "x² = 16x + 225\r\n" );
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document.write( "x² - 16x - 225 = 0\r\n" );
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document.write( "(x - 25)(x + 9) = 0\r\n" );
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document.write( "x - 25 =  0      x + 9 =  0\r\n" );
document.write( "     x = 25          x = -9 \r\n" );
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document.write( "We must always check a radical equation\r\n" );
document.write( "Checking x = 25:\r\n" );
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document.write( "      _________\r\n" );
document.write( " x = √16x + 225\r\n" );
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document.write( "25 = √16(25) + 225\r\n" );
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document.write( "25 = √400 + 225\r\n" );
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document.write( "25 = √625\r\n" );
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document.write( "25 = 25\r\n" );
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document.write( "So x = 25 is a solution.\r\n" );
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document.write( "Checking x = -9:\r\n" );
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document.write( "      _________\r\n" );
document.write( " x = √16x + 225\r\n" );
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document.write( "-9 = √16(-9) + 225\r\n" );
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document.write( "-9 = √-144 + 225\r\n" );
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document.write( "-9 = √81\r\n" );
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document.write( "-9 = 9\r\n" );
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document.write( "That is false, so x = -9 is not a solution.  (But please don't get\r\n" );
document.write( "the idea that you discarded -9 because it is negative, as in\r\n" );
document.write( "many cases a negative solution checks. It just didn't happen to\r\n" );
document.write( "in this case).\r\n" );
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document.write( "Edwin
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