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Help. ​

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Help.

Feb 1, 2018

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5.  These are a little more difficult than what you have done before, NSS

First....we would like to separate the radical terms....so......add √x to both sides

√ [ 5x + 1 ]  =  5 + √x          square both sides

5x + 1  =  (5 + √x)^2

5x + 1  =   ( 5 + √x ) ( 5 + √x)   simplify

5x + 1  =  25  + 5√x + 5√x  +  x

5x + 1   =  25 + 10√x  +  x

We want the radical on one side....so.....subtract 25, x from both sides

4x - 24  =  10√x       divide through by 2 to reduce the size of the numbers

2x -  12  = 5√x

2 ( x - 6)  =  5√x          square both sides, again

2^2 (x - 6)^2  =  25x

4 (x - 6) ( x - 6)  =  25x

4 ( x^2 - 12x + 36)  =  25x

4x^2 - 48x + 144  = 25x      subtract 25 x from  both sides

4x^2 -  73x + 144  =  0    using the quadratic formula, the solutions to this are

x  = 9/4     or  x  =16

Since 9/4 isn't on the answer sheet......16 must be the only possible solution  !!!!!

Plug this into the original equation to make sure......!!!!

NSS.....I don't often recommend this....but...on a test.....because of the lengthy nature of this type of problem...I might be tempted to just plug the choices into the original equation to see which one was correct!!!!

Feb 1, 2018
edited by CPhill  Feb 1, 2018