SOLUTION: a number is added to five time its reciprocal is -6. Find the number.

Question 535600: a number is added to five time its reciprocal is -6. Find the number.
Answer by bucky(2189) (Show Source): You can put this solution on YOUR website!
As you described it, the problem you are trying to solve is:
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Get rid of the denominator by multiplying both sides of the equation (all terms) by x and you have:
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Note that the first term on the left side becomes .
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Also note that in the second term on the left side, you can cancel the multiplier x with the denominator x. After these two actions the equation becomes:
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which simplifies to:
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Get rid of the -6x on the right side by adding +6x to both sides to get:
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This quadratic equation can be factored as shown below:
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Note that this equation will be true if either of the factors is equal to zero. If either factor is equal to zero the left side will have a multiplication by zero and will, therefore, equal the zero on the right side.
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So we can solve this equation by finding what numbers will make the two factors equal to zero. Do this by setting each factor (one at a time) equal to zero to get:
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which is solved by subtracting 5 from both sides to get x = -5
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and
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which is solved by subtracting 1 from both sides to get x = -1
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Your problem has two correct answers. They are x = -5 and x = -1.
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You can check these answers by returning to the original problem and substituting these values one at a time for x.
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set x = -5 and you have:
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and this simplifies to which is true.
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Then set x = -1 and you have:
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and this simplifies to which is also true.
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Both answers are OK because they make the original problem true.
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Hope this helps you to understand the problem.
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