SOLUTION: Please help w/ the following: Solve x^2/2 - 5x/4 = -3/4 Thank you.

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Question 55251: Please help w/ the following:
Solve
x^2/2 - 5x/4 = -3/4
Thank you.
Answer by funmath(2933) About Me  (Show Source):
You can put this solution on YOUR website!
Solve
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.
4%28x%5E2%2F2%29%2B4%28-5x%2F4%29=4%28-3%2F4%29
%284%2F2%29x%5E2%2B%284%2F4%29%28-5x%29=%284%2F4%29%28-3%29
2x%5E2-5x=-3 Set the problem = to 0.
2x%5E2-5x%2B3=-3%2B3
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
-2*-3=6 and -2-3=-5
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)
2x%5E2%2B%28-2-3%29x%2B3=0
2x%5E2-2x-3x%2B3=0
%282x%5E2-2x%29%2B%28-3x%2B3%29=0
2x%28x-1%29-3%28x-1%29=0
%282x-3%29%28x-1%29=0 Use the zero product property and set each parenthesis=0 and solve for x.
2x-3=0 and x-1=0
2x-3%2B3=0%2B3 and x-1%2B1=0%2B1
2x=3 and x=1
2x%2F2=3%2F2 and x=1
x=3%2F2 and x=1
Some books write the solution set as x={1,3/2}
Happy Calculating!!!