document.write( "Question 55251: Please help w/ the following:
\n" ); document.write( "Solve
\n" ); document.write( "x^2/2 - 5x/4 = -3/4
\n" ); document.write( "Thank you. \n" ); document.write( "

Algebra.Com's Answer #37503 by funmath(2933) $\"\"$ $\"About$

You can put this solution on YOUR website!
Solve
\n" ); document.write( " $\"x%5E2%2F2+-+5x%2F4+=+-3%2F4\"$ I hate fractions, don't you? Let's obliterate them by multiplying both sides of the = sign by the LCD, 4.
\n" ); document.write( " $\"4%28x%5E2%2F2%29%2B4%28-5x%2F4%29=4%28-3%2F4%29\"$
\n" ); document.write( " $\"%284%2F2%29x%5E2%2B%284%2F4%29%28-5x%29=%284%2F4%29%28-3%29\"$
\n" ); document.write( " $\"2x%5E2-5x=-3\"$ Set the problem = to 0.
\n" ); document.write( " $\"2x%5E2-5x%2B3=-3%2B3\"$
\n" ); document.write( " $\"2x%5E2-5x%2B3=0\"$ This quadratic equation is in standard form $\"highlight%28ax%5E2%2Bbx%2Bc%29\"$ Factor, we need to find two integers that multiply to get a*c but add to get b. Our a=2, b=-5, and c=3, a*c=6
\n" ); document.write( "-2*-3=6 and -2-3=-5
\n" ); document.write( "Replace b with -2-3 and factor by grouping:(there are other ways to do that, but this is easier to explain via the internet)
\n" ); document.write( " $\"2x%5E2%2B%28-2-3%29x%2B3=0\"$
\n" ); document.write( " $\"2x%5E2-2x-3x%2B3=0\"$
\n" ); document.write( " $\"%282x%5E2-2x%29%2B%28-3x%2B3%29=0\"$
\n" ); document.write( " $\"2x%28x-1%29-3%28x-1%29=0\"$
\n" ); document.write( " $\"%282x-3%29%28x-1%29=0\"$ Use the zero product property and set each parenthesis=0 and solve for x.
\n" ); document.write( " $\"2x-3=0\"$ and $\"x-1=0\"$
\n" ); document.write( " $\"2x-3%2B3=0%2B3\"$ and $\"x-1%2B1=0%2B1\"$
\n" ); document.write( " $\"2x=3\"$ and $\"x=1\"$
\n" ); document.write( " $\"2x%2F2=3%2F2\"$ and $\"x=1\"$
\n" ); document.write( " $\"x=3%2F2\"$ and $\"x=1\"$
\n" ); document.write( "Some books write the solution set as x={1,3/2}
\n" ); document.write( "Happy Calculating!!!
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