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Question 359969: Hi there, I'm reviewing for a test and not quite sure how to solve the following problem:
3x - 2sqrt(x) - 5 = 0
In other examples I worked on, I moved the loose number to the other side and squared both sides. When doing this, I'm not sure how to multiply 3x * 2sqrt(x) to solve, or if that's even the right thing to do here. I'm stumped. Any help/guidance you can provide is greatly appreciated!
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! 3x - 2sqrt(x) - 5 = 0
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This is a quadratic with variable = sqrt(x).
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Let sqrt(x) = w
Then x = w^2
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Substitute to get:
3w^2 - 2w - 5 = 0
Factor:
3w^2-5w+3w-5 = 0
w(3w-5) + (3w-5) = 0
(3w-5)(w+1) = 0
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w = 5/3 or w = -1
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Substitute and solve for "x":
sqrt(x) = 5/3 or sqrt(x) = -1
x = (25/9) or x = 1
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x-1 is an extraneous root.
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x = 25/9 is the only solution.
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Cheers,
stan H.
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