document.write( "Question 520709: What are all ordered pairs of real numbers (x, y) for which
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Algebra.Com's Answer #346206 by Edwin McCravy(20055)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "17x² – 10xy + 2y² – 6x + 2 = 0\r\n" );
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document.write( "Rearrange the terms in descending order of y\r\n" );
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document.write( "2y² - 10xy + 17x² - 6x + 2 = 0\r\n" );
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document.write( "Think of it like this:\r\n" );
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document.write( "2y² + (-10x)y + (17x² - 6x + 2) = 0 \r\n" );
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document.write( "and use the quadratic formula\r\n" );
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document.write( "with a = 2, b = -10x and c = 17x² - 6x + 2\r\n" );
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document.write( "y = \"%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+\"\r\n" );
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document.write( "y = \"%28-%28-10x%29+%2B-+sqrt%28+%28-10x%29%5E2-4%2A%282%29%2A%2817x%5E2-6x%2B2%29+%29%29%2F%282%2A%282%29%29+\"\r\n" );
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document.write( "y = \"%2810x+%2B-+sqrt%28100x%5E2-8%2817x%5E2-6x%2B2%29+%29%29%2F4+\"\r\n" );
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document.write( "y = \"%2810x+%2B-+sqrt%28100x%5E2-136x%5E2%2B48x-16+%29%29%2F4+\"\r\n" );
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document.write( "y = \"%2810x+%2B-+sqrt%28-36x%5E2%2B48x-16+%29%29%2F4+\"\r\n" );
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document.write( "y = \"%2810x+%2B-+sqrt%28-4%289x%5E2-12x%2B4%29+%29%29%2F4+\"\r\n" );
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document.write( "y = \"%2810x+%2B-+sqrt%28-4%283x-2%29%283x-2%29+%29%29%2F4+\"\r\n" );
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document.write( "y = \"%2810x+%2B-+sqrt%28-4%283x-2%29%5E2%29%29%2F4+\" \r\n" );
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document.write( "y = \"%2810x+%2B-+2i%2Asqrt%28%283x-2%29%5E2%29%29%2F4+\" \r\n" );
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document.write( "Divide every term in the top and bottom by 2\r\n" );
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document.write( "y = \"%285x+%2B-+i%2Asqrt%28%283x-2%29%5E2%29%29%2F2+\"\r\n" );
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document.write( "y = \"%285x+%2B-+i%2Aabs%283x-2%29%29%2F2+\"\r\n" );
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document.write( "That will be imaginary unless the imaginary part is 0, so\r\n" );
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document.write( "3x-2 = 0\r\n" );
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document.write( "   x = \"2%2F3\"\r\n" );
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document.write( "Substitute that\r\n" );
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document.write( "y = \"%285%282%2F3%29%29%2F2+\" = \"%2810%2F3%29%2F2\" = \"10%2F3\"÷2 = \"5%2F3\"\r\n" );
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document.write( "and get y = \"5%2F3\"\r\n" );
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document.write( "Answer:  (\"2%2F3\",\"5%2F3\")\r\n" );
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document.write( "Edwin
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