document.write( "Question 608368: What is x^2+2y^2+6x-20y+53=0 in standard form? \n" ); document.write( "

Algebra.Com's Answer #383171 by Edwin McCravy(20060) $\"\"$ $\"About$

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document.write( "x² + 2y² + 6x - 20y + 53 = 0\r\n" );
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document.write( "Rearrange the terms as\r\n" );
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document.write( "x² + 6x + 2y² - 20y = -53 \r\n" );
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document.write( "Complete the square of the first two terms:\r\n" );
document.write( "Multiply 6 by  getting 3\r\n" );
document.write( "Square 3, getting +9\r\n" );
document.write( "Add +9 to both sides\r\n" );
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document.write( "x² + 6x + 9 + 2y² - 20y = -53+9\r\n" );
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document.write( "Factor the first three terms x²+6x+9 as (x+3)(x+3) or (x+3)²\r\n" );
document.write( "and combine the terms on the right:\r\n" );
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document.write( "(x + 3)² + 2y² - 20y = -44 \r\n" );
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document.write( "Factor 2 out of the last two terms on the left:\r\n" );
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document.write( "(x + 3)² + 2y² - 20y = -44\r\n" );
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document.write( "(x + 3)² + 2(y² - 10y) = -44\r\n" );
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document.write( "Complete the square of the two terms inside the\r\n" );
document.write( "second parentheses:\r\n" );
document.write( "Multiply -10 by  getting -5\r\n" );
document.write( "Square -5, getting +25\r\n" );
document.write( "Add +25 inside the second parentheses and since there\r\n" );
document.write( "is a 2 coefficient, we are really adding 2 times +25 or\r\n" );
document.write( "+50 to both sides, so we add +50 to the right sides:\r\n" );
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document.write( "(x + 3)² + 2(y² - 10y + 25) = -44 + 50\r\n" );
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document.write( "Factor the three terms y²-10y+25 as (y-5)(y-5) or (y-5)²\r\n" );
document.write( "and combine the terms on the right:\r\n" );
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document.write( "(x + 3)² + 2(y - 5)² = 6\r\n" );
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document.write( "Get 1 on the right by dividing all terms by 6\r\n" );
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document.write( " +  = \r\n" );
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document.write( " +  = 1\r\n" );
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document.write( "Edwin

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