SOLUTION: Two numbers that have a product of -840 and the sum is -22.

Question 476080: Two numbers that have a product of -840 and the sum is -22.
Answer by bucky(2189) (Show Source): You can put this solution on YOUR website!
Let the two numbers be x and y.
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The product of the two numbers is -840. In equation form this is:
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<---- first equation
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The sum of the two numbers is -22. In equation form this is:
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<---- second equation
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In the second equation solve for one of the variables in terms of the other. For example solve for x by subtracting y from both sides of the equation. When you do this subtraction you get:
.

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Substitute the right side of this equation for x in the first equation. This substitution leads to:
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Multiply out the left side by multiplying y times each of the two terms in parentheses to get:
.

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add 840 to both sides of this equation and you have:
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To get this into standard quadratic form, multiply both sides (all terms) by -1 and the result is:
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You can solve this by using the quadratic formula, or you can factor it. The left side factors as shown:
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in which case or
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in which case
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Since you now know possible solutions for y, you can return to the second equation and solve for x. Using the second equation, substitute y = -42 and you get for x:
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Add +42 to both sides and this becomes:
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which simplifies to:
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So one possible solution to this problem is x = 20 and y = -42
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Another possible solution occurs when y = +20. You can work this out by solving for x, but you will find that the answer for x is x = -42.
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The answer now becomes apparent. One of the two numbers is -42 and the other is +20. (Either x = 20 and y = -42 or y = 20 and x = -42).
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Hope this helps you to understand the process for solving this problem.
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