Question 73546
{{{2x^2-x=6}}}
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The standard form for a quadratic equation is:
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{{{ax^2 + bx + c = 0}}}
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You need to put your problem into that format.  Note that the only difference is that your
problem has a constant on the right side instead of a zero.  So let's get rid of the 6 
on the right side by subtracting 6 from both sides of the equation.  When you do that subtraction
the result is:
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{{{2x^2 - x - 6 = 0}}}
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There are several ways to solve this equation.  One of the ways is to find out if the 
equation can be factored.  Start by recognizing that the factors would have to have the
first terms look like:
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(2x   )*(x     )
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You have to find the numbers in each set of parenthesis that will make the factors multiply
to give you back the equation of the problem.
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Now look at the factors of 6.  There are two sets of them ... 6*1 and 3*2.  Because 
the 6 in the equation has a minus sign, one of the factors has to be negative. Notice in
the equation that the middle term is minus x.  Whatever we select for the numbers in
the factors will have to work together to give a minus -6 as the last number in the equation 
and a -x as the middle term.  Some trial and error is involved until you get enough 
experience to find a rapid way to do this. To save you some time the factors are:
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{{{(2x + 3)*(x - 2)}}}
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If you multiply these two together you get {{{2x^2 - x - 6}}}. So the factors can be
substituted for the left side our equation to get:
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{{{(2x + 3)*(x - 2)= 0}}}
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Note that if either factor on the left side is zero, it makes the left side of the equation
equal the right side. (zero = zero)
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Set the two factors (one at a time) equal to zero and solve for the value of x that makes
it happen.  
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{{{2x + 3 = 0 }}}
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Subtract 3 from both sides and then divide that result by 2.  You will find that {{{x = -3/2}}}
is one solution to the problem.
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Next set the other factor equal to zero and you get {{{x - 2 = 0}}}.  Add 2 to both sides
and you get {{{x = 2}}} as the second solution.
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So the answers to this problem are {{{x = -3/2}}} and {{{x = 2}}}.
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Hope that this gives you a feel for one way to do these problems ... by factoring
if the equation can be factored.