Question 73271
Solve:
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{{{10x^2+9x=-2}}}
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The first thing to do is to add +2 to both sides of this equation to eliminate the -2 on the
right side and get the standard quadratic form of:
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{{{10x^2 + 9x + 2 = 0}}}
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There are several ways you can solve this equation.  
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For example your can graph {{{y = 10x^2 +9x+2}}} and the values of x that you are looking for
will be at the points where the graph crosses the x-axis.
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Or you can factor the equation, if it is easily factored.  (This one can be factored.)
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Or you can use the quadratic formula.
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Usually the order in which you learn to do these is just as listed above.  I'm going to
assume that you understand how to factor.  The factors for the {{{10x^2}}} term are either
(10x and x) or (5x and 2x).  And the factors of the constant {{{2}}} are (2 and 1). Now all
you have to do is to figure out what combination of numbers and signs will result in a 
middle term of 9x.
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You can do the detailed work and thought, but I'll tell you that the answer is:
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{{{(2x + 1)*(5x + 2)}}}
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Put these back into the equation to get:
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{{{(2x + 1)*(5x + 2)=0}}}
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This equation will be true if either one of the factors equals zero because a factor of
zero on the left side will make the whole left side zero, and that will equal the right side.
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So, set:
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{{{2x +1 = 0}}}
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and solve by first subtracting 1 from both sides to get:
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{{{2x = -1}}}
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Finally divide both sides by 2 and you find that:
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{{{x = -1/2}}}
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But the other factor can be zero also.  So this time let the other factor equal zero and solve:
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{{{5x + 2 = 0}}}
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Subtract 2 from both sides to find that:
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{{{5x = -2}}}
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Then divide both sides by 5 to get:
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{{{x = -2/5}}}
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So the two answers to this problem are {{{x = -1/2}}} and {{{x = -2/5}}}.
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Hope that this answers your question in a method you understand.  Graphing to solve this
would be a little time consuming because the answers are not "nice" (because they are not
integers). The quadratic formula is a good method to solve any quadratic equation, but
it can be a little challenging if you have not at least studied it a little.