+130116 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!!!!
