document.write( "Question 48549: What three techniques can be used to solve a quadratic equation? Demonstrate these techniques on the equation \"12x^2 - 10x - 42 = 0\". \n" ); document.write( "

Algebra.Com's Answer #32136 by Nate(3500) $\"\"$ $\"About$

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1.)Graphing (at most times, not very accurate)
\n" ); document.write( " $\"graph%28600%2C600%2C-10%2C10%2C-10%2C10%2C12x%5E2-10x-42%2C0%29\"$
\n" ); document.write( "2.)Factoring
\n" ); document.write( " $\"12x%5E2+-+10x+-+42+=+0\"$
\n" ); document.write( " $\"6x%5E2+-+5x+-+21+=+0\"$
\n" ); document.write( " $\"6x%5E2+%2B+9x+-+14x+-+21+=+0\"$
\n" ); document.write( " $\"%286x%5E2+%2B+9x%29+%2B+%28-14x+-+21%29+=+0\"$
\n" ); document.write( " $\"3x%282x+%2B+3%29+-+7%282x+%2B+3%29+=+0\"$
\n" ); document.write( " $\"%283x+-+7%29%282x+%2B+3%29+=+0\"$
\n" ); document.write( "3x - 7 = 0
\n" ); document.write( "3x = 7
\n" ); document.write( "x = 7/3 or 2 1/3
\n" ); document.write( "and
\n" ); document.write( "2x + 3 = 0
\n" ); document.write( "2x = -3
\n" ); document.write( "x = -3/2 or -1 1/2
\n" ); document.write( "3.)Completing the Square
\n" ); document.write( " $\"12x%5E2+-+10x+-+42+=+0\"$
\n" ); document.write( " $\"6x%5E2+-+5x+-+21+=+0\"$
\n" ); document.write( " $\"x%5E2+-+5x%2F6+=+7%2F2\"$
\n" ); document.write( " $\"%28x+-+5%2F12%29%5E2+=+25%2F144+%2B+504%2F144+=+529%2F144\"$
\n" ); document.write( " $\"x+-+5%2F12\"$ = +- $\"23%2F12\"$
\n" ); document.write( " $\"x+=+5%2F12+%2B-+23%2F12\"$
\n" ); document.write( " $\"x+=+%285+%2B-+23%29%2F12\"$
\n" ); document.write( "4.)Quadratic Formula
\n" ); document.write( " $\"x+=+%28-b+%2B-+sqrt%28+b%5E2+-+4%2Aa%2Ac+%29%29%2F%282%2Aa%29+\"$
\n" ); document.write( " $\"x+=+%285+%2B-+sqrt%28+25+%2B+504+%29%29%2F%2812%29+\"$
\n" ); document.write( " $\"x+=+%285+%2B-+23%29%2F12\"$ \n" ); document.write( "

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