SOLUTION: Could someone please help me with solving the following equation: 10x^2+9x=-2 Thanks

Question 73271: Could someone please help me with solving the following equation:
10x^2+9x=-2
Thanks
Answer by bucky(2189) (Show Source): You can put this solution on YOUR website!
Solve:
.

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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:
.

.
There are several ways you can solve this equation.
.
For example your can graph and the values of x that you are looking for
will be at the points where the graph crosses the x-axis.
.
Or you can factor the equation, if it is easily factored. (This one can be factored.)
.
Or you can use the quadratic formula.
.
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 term are either
(10x and x) or (5x and 2x). And the factors of the constant 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.
.
You can do the detailed work and thought, but I'll tell you that the answer is:
.

.
Put these back into the equation to get:
.

.
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.
.
So, set:
.

.
and solve by first subtracting 1 from both sides to get:
.

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Finally divide both sides by 2 and you find that:
.

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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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Subtract 2 from both sides to find that:
.

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Then divide both sides by 5 to get:
.

.
So the two answers to this problem are and .
.
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.

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