SOLUTION: 3x + 14{{{ sqrt( x ) }}} = 5 Can you help me solve this?

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons -> SOLUTION: 3x + 14{{{ sqrt( x ) }}} = 5 Can you help me solve this?      Log On


   

Question 992751: 3x + 14+sqrt%28+x+%29+ = 5
Can you help me solve this?
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
3x + 14sqrt( x ) = 5
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3(sqrt(x))^2 + 14sqrt(x) - 5 = 0
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Let w = sqrt(x)
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Rewrite your quadratic as::
3w^2 + 14w - 5 = 0
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Factor::
3w^2 + 15w-w -5 = 0
3w(w+5)-(w+5) = 0
(w+5)(3w-1) = 0
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w = -5 or w = 1/3
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Now, solve for "x"
sqrt(x) = -5 or sqrt(x) = 1/3
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x = 25 or is extraneous since sqrt(25) = 5, by definition; or x = 1/9
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Cheers,
Stan H.
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