document.write( "Question 120255: Bill used completing the square to find the zeroes of the function $\"y=9x%5E2-12x-33\"$ . How is this done ? \n" ); document.write( "

Algebra.Com's Answer #88140 by Edwin McCravy(20055) $\"\"$ $\"About$

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SOLUTION BY EDWIN:\r
\n" ); document.write( "\n" ); document.write( "Bill used completing the square to find the zeroes of the function
\n" ); document.write( " $\"y=9x%5E2-12x-33\"$ . How is this done ?
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document.write( "It's long! Sorry!\r\n" );
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document.write( "y = 9x² - 12x - 33\r\n" );
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document.write( "To find the zeros we substitute 0 for y and solve for x:\r\n" );
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document.write( "0 = 9x² - 12x - 33\r\n" );
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document.write( "Let's put the 0 on the right:\r\n" );
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document.write( "9x² - 12x - 33 = 0\r\n" );
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document.write( "1. Isolate the terms in x on the left:\r\n" );
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document.write( "That is, add 33 to both sides:\r\n" );
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document.write( "    9x² - 12x = 33\r\n" );
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document.write( "2. Divide every term through by the coefficient\r\n" );
document.write( "   of x², since it is not 1.\r\n" );
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document.write( "    x² - x = \r\n" );
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document.write( "Simplifying:\r\n" );
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document.write( "    x² - x = \r\n" );
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document.write( "3. To the side multiply the coefficient of x by \r\n" );
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document.write( "      =  = \r\n" );
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document.write( "4.  Square the result of step 3:\r\n" );
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document.write( "      = \r\n" );
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document.write( "5.  Add that to both sides of the equation we \r\n" );
document.write( "    had at the end of step 2:\r\n" );
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document.write( "    x² - x +  = +\r\n" );
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document.write( "6.  Factor the left side:\r\n" );
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document.write( "    {x - )(x - ) = +\r\n" );
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document.write( "7.  Combine the terms on the right sides\r\n" );
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document.write( "    Write  as \r\n" );
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document.write( "    {x - )(x - ) = +\r\n" );
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document.write( "    {x - )(x - ) = \r\n" );
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document.write( "8. Write the left side as a square.  We always can.  That's\r\n" );
document.write( "   why the method is called \"completing the square\".\r\n" );
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document.write( "    {x - )² = \r\n" );
document.write( "  \r\n" );
document.write( "10. Use the principle of square roots:\r\n" );
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document.write( "       x -  = ±\r\n" );
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document.write( "11. Solve for x.\r\n" );
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document.write( "                   x =  ± \r\n" );
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document.write( "That can be written:\r\n" );
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document.write( "                   x = \r\n" );
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document.write( "Edwin

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