Question 556104: Hello, I am struggling with this homework problem. I need to solve for "x" of course, but I can't seem to get "x" on one side of the equation, by itself. Of course I have found "solvers" on Google which give me the answer, but I need to understand the methods/steps in this equation so I can do it again later. I would really appreciate if somebody can help me here! Thank you so much!
1000/x = (100*0.98)+(4.9*x)
Brent
Answer by bucky(2189)   (Show Source):
You can put this solution on YOUR website! Hi Brent --- Welcome to Algebra.com
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The problem you were given to solve is:
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Just to make things a little easier, let's multiply out the first term on the right side by multiplying 100 times 0.98 which results in, of course, 98. So we replace this product with 98 and the equation then becomes:
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We can also remove the parentheses around the second term on the right and we have:
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Next, let's get rid of the denominator x on the left side by multiplying both sides of the equation (all terms) by x to get:
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On the left side the x in the numerator cancels with the x in the denominator. And on the right side the second term contains x times x and that is x squared. So we have converted the equation to:
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Now eliminate the 1000 on the left side by subtracting 1000 from both sides and we have:
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We then can rearrange the terms on the right side in descending powers of x to get:
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And finally we can put this equation into the standard form of a quadratic equation by simply switching sides (transposing) and we have:
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This is in the standard quadratic form of:
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in which a = 4.9, b = 98, and c = -1000. We can solve this using the quadratic formula which says that in this form of an equation, the value of x is given by:
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Substituting the values we have for a, b, and c gives us:
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98 squared is 9604. -4 times 4.9 times -1000 is 19,600. And 2 times 4.9 is 9.8. Substitute these values into the equation for x and we have:
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Add the two numbers under the radical and the equation simplifies to:
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Take the square root of 29204 on a calculator and we get that it equals 170.8917786. Replace the square root with that value and we then have:
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Divide the denominator (9.8) into each of these terms and we have:
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From this we get two answers for x as follows:
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which results in:
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and then:
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which gives us:
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To check these two answers we can one at a time substitute these two values for x back into the original equation as follows:
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<------original equation
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 <-- with x = 7.43793659
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and
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 <-- with x = -27.43793659
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If we do the math we will find that in these two equations the left side will equal the right side. This means our two answers for x are correct.
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Hope this helps you to see your way through this problem.
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