document.write( "Question 703926: i need to solve x-2√x-80=0 \n" ); document.write( "
Algebra.Com's Answer #433790 by Edwin McCravy(20060)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "x - 2√x - 80 = 0\r\n" );
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document.write( "There are two ways to solve this:\r\n" );
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document.write( "Method 1:  By u-substitution:\r\n" );
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document.write( "let u = √x\r\n" );
document.write( "then u² = x\r\n" );
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document.write( "Substitute u² for x and u for √x\r\n" );
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document.write( "u² - 2u - 80 = 0\r\n" );
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document.write( "That factors as:\r\n" );
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document.write( "(u - 10)(u + 8) = 0\r\n" );
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document.write( "u = 10, u = -8\r\n" );
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document.write( "Substitute √x for u\r\n" );
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document.write( "   √x = 10           √x = -8\r\n" );
document.write( "(√x)² = 10²       (√x)² = (-8)²\r\n" );
document.write( "    x = 100           x = 64\r\n" );
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document.write( "Check for extraneous solution(s):\r\n" );
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document.write( "     x - 2√x - 80 = 0\r\n" );
document.write( " 100 - 2√100 - 80 = 0\r\n" );
document.write( " 100 - 2(10) - 80 = 0\r\n" );
document.write( "    100 - 20 - 80 = 0\r\n" );
document.write( "                0 = 0\r\n" );
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document.write( "That's true, so x=10 is a solution.\r\n" );
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document.write( "     x - 2√x - 80 = 0\r\n" );
document.write( "   64 - 2√64 - 80 = 0\r\n" );
document.write( "   64 - 2(8) - 80 = 0\r\n" );
document.write( "     64 - 16 - 80 = 0\r\n" );
document.write( "              -32 = 0\r\n" );
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document.write( "That's false, so the only solution is x=10\r\n" );
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document.write( "Method 2:  By isolating the radical term and squaring\r\n" );
document.write( "both sides:\r\n" );
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document.write( "    x - 2√x - 80 = 0\r\n" );
document.write( "          x - 80 = 2√x\r\n" );
document.write( "       (x - 80)² = 4(√x)²\r\n" );
document.write( "x² - 160x + 6400 = 4x \r\n" );
document.write( "x² - 164x + 6400 = 0\r\n" );
document.write( "   (x-100)(x-64) = 0\r\n" );
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document.write( "x = 100, x = 64\r\n" );
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document.write( "Check for extraneous solution(s):\r\n" );
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document.write( "     x - 2√x - 80 = 0\r\n" );
document.write( " 100 - 2√100 - 80 = 0\r\n" );
document.write( " 100 - 2(10) - 80 = 0\r\n" );
document.write( "    100 - 20 - 80 = 0\r\n" );
document.write( "                0 = 0\r\n" );
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document.write( "That's true, so x=10 is a solution.\r\n" );
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document.write( "     x - 2√x - 80 = 0\r\n" );
document.write( "   64 - 2√64 - 80 = 0\r\n" );
document.write( "   64 - 2(8) - 80 = 0\r\n" );
document.write( "     64 - 16 - 80 = 0\r\n" );
document.write( "              -32 = 0\r\n" );
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document.write( "That's false, so the only solution is x=10\r\n" );
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document.write( "Edwin
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