You can put this solution on YOUR website! Given:
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Get this into the more standard form of a quadratic equation by subtracting 20y from both
sides to eliminate the 20y on the right side. When you do that subtraction the result is:
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Now the problem is to see if the left side of this equation can be factored. (Since the
problem asks you to use the zero-factor property you can proceed under the assumption
that it will factor.)
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The factors of the first term () are either (25y and y) or (5y and 5y). The factors
of the last term are either (4 and 1) or (2 and 2). The problem is to find a combination
of these factors that will produce as the middle term. And if you set up
two factors and try various combinations of values you will find that the factors that
work are:
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and this product is to equal zero so the equation becomes:
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and because both factors are the same, this can be simplified to:
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This equation will be true if the factor (5y -2) equals zero. Setting this up results in
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Add 2 to both sides to eliminate the -2 on the left side and the result is:
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and then divide both sides by 5 to get:
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This is the solution to the problem. You can verify that it is correct by returning to
the original equation and substituting for y to verify that
this value of y will make the left side of the equation equal the right side.
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Hope this helps you to understand the problem a little better. The most difficult
part of the problem involves the trial-and-error involved with finding the correct combination
of values that will produce -20y for the middle term of the quadratic.
(