document.write( "Question 1207630: Find the real solutions of each equation.\r
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Algebra.Com's Answer #845604 by Edwin McCravy(20055)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "\"sqrt%2810+%2B+sqrt%28x%29%29+=+sqrt%28x%29\"\r\n" );
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document.write( "Square both sides:\r\n" );
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document.write( "\"10+%2B+sqrt%28x%29+=+x\"\r\n" );
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document.write( "Isolate the root:\r\n" );
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document.write( "\"sqrt%28x%29+=+x-10\"\r\n" );
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document.write( "Square both sides:\r\n" );
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document.write( "\"x=x%5E2-20x%2B100\"\r\n" );
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document.write( "\"x%5E2-21x%2B100\"\r\n" );
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document.write( "\"x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+\"\r\n" );
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document.write( "\"x+=+%28-%28-21%29+%2B-+sqrt%28+%28-21%29%5E2-4%2A1%2A100+%29%29%2F%282%2A1%29+\"\r\n" );
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document.write( "\"x+=+%2821+%2B-+sqrt%28441-400+%29%29%2F2+\"\r\n" );
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document.write( "\"x+=+%2821+%2B-+sqrt%2841%29%29%2F2+\"\r\n" );
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document.write( "But when you square both sides of an equation, you have to check your answers,\r\n" );
document.write( "for some, or even ALL, of your answers may be extraneous.\r\n" );
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document.write( "So we check.  It would be very time consuming to check the answers in exact\r\n" );
document.write( "form, so get their decimal approximations. \r\n" );
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document.write( "\"x+=+%2821+%2B+sqrt%2841%29%29%2F2+\" is approximately 13.70156212\r\n" );
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document.write( "\"sqrt%2810+%2B+sqrt%28x%29%29+=+sqrt%28x%29\"\r\n" );
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document.write( "\"sqrt%2810+%2B+sqrt%2813.70156212%29%29+=+sqrt%2813.70156212%29\"\r\n" );
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document.write( "\"sqrt%2810+%2B+3.701562119%29+=+3.701562119\"\r\n" );
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document.write( "\"sqrt%2813.701562119%29+=+3.701562119\"\r\n" );
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document.write( "\"3.701562119%29+=+3.701562119\"\r\n" );
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document.write( "That checks, so we know that is a solution.\r\n" );
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document.write( "Now let's check the other solution\r\n" );
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document.write( "\"x+=+%2821+-+sqrt%2841%29%29%2F2+\" is approximately 3.701562119\r\n" );
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document.write( "\"sqrt%2810+%2B+sqrt%28x%29%29+=+sqrt%28x%29\"\r\n" );
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document.write( "\"sqrt%2810+%2B+sqrt%283.701562119%29%29+=+sqrt%283.701562119%29\"\r\n" );
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document.write( "\"sqrt%2810+%2B+1.923944417%29+=+1.923944417\"\r\n" );
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document.write( "\"sqrt%2811.923944417%29+=+1.923944417\"\r\n" );
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document.write( "\"3.453106488+=+1.923944417\"\r\n" );
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document.write( "As we see, this does not check, so there is only 1 solution,\r\n" );
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document.write( "\"x+=+%2821+%2B+sqrt%2841%29%29%2F2+\"\r\n" );
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document.write( "Edwin
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