document.write( "Question 30038: 3x^2 - 2x - 3 = 0
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Algebra.Com's Answer #16789 by AnlytcPhil(1806) $\"\"$ $\"About$

You can put this solution on YOUR website!

3x^2 - 2x - 3 = 0\r\n" );
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document.write( "By completing the square\r\n" );
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document.write( "3x² - 2x - 3 = 0\r\n" );
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document.write( "Get constant term on right by adding 3 to both sides\r\n" );
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document.write( "3x² - 2x = 3\r\n" );
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document.write( "Divide every term by the coefficient of x², namely 3\r\n" );
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document.write( " 3        2       3\r\n" );
document.write( "--- x² - --- x = ---\r\n" );
document.write( " 3        3       3\r\n" );
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document.write( "          2     \r\n" );
document.write( "    x² - --- x = 1\r\n" );
document.write( "          3\r\n" );
document.write( "or written on one line\r\n" );
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document.write( "    x² - (2/3)x = 1\r\n" );
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document.write( "Multiply coefficient of x, -2/3 by 1/2, getting -1/3\r\n" );
document.write( "Square -1/3:   (-1/3)2 = 1/9\r\n" );
document.write( "Add 1/9 to both sides:\r\n" );
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document.write( "x² - (2/3)x + 1/9 = 1 + 1/9\r\n" );
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document.write( "The left side factors as\r\n" );
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document.write( "(x - 1/3)(x - 1/3) = 1 + 1/9\r\n" );
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document.write( "or\r\n" );
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document.write( "(x - 1/3)² = 1 + 1/9\r\n" );
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document.write( "The right side becomes 1 + 1/9 = 9/9 + 1/3 = 10/3\r\n" );
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document.write( "(x - 1/3)² = 10/9\r\n" );
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document.write( "Take the square root of both sides, remembering ± \r\n" );
document.write( "on the right side\r\n" );
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document.write( "x - 1/3 = ±Ö10/9\r\n" );
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document.write( "We can take the square root of denominator 9 as 3\r\n" );
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document.write( "x - 1/3 = ±Ö10/3\r\n" );
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document.write( "Solving for x by adding 1/3 to both sides\r\n" );
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document.write( "x = 1/3 ± Ö10/3\r\n" );
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document.write( "Both fractions have same denominator, so combine\r\n" );
document.write( "numerators over the common denominator\r\n" );
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document.write( "x = (1 ± Ö10)/3\r\n" );
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document.write( "Edwin\r\n" );
document.write( "AnlytcPhil@aol.com

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