SOLUTION: Hi! Solve the equation (1+sqrt(x))^2-2(1+sqrt(x))-15=0 thanks!

Algebra ->  Equations -> SOLUTION: Hi! Solve the equation (1+sqrt(x))^2-2(1+sqrt(x))-15=0 thanks!       Log On


   

Question 198474: Hi!
Solve the equation (1+sqrt(x))^2-2(1+sqrt(x))-15=0
thanks!

Found 2 solutions by arallie, MRperkins:
Answer by arallie(162) About Me  (Show Source):
Answer by MRperkins(300) About Me  (Show Source):
You can put this solution on YOUR website!
There is probably more than one way to solve this, but the easiest way is actually quite easy and I am sure you will understand it once we are done.
First, notice that the first term is %281%2Bsqrt%28x%29%29%5E2 and the second term is -2%2A%281%2Bsqrt%28x%29%29
Now, select any variable to replace 1%2Bsqrt%28x%29 let's say z
so now substitute z for 1%2Bsqrt%28x%29 and you get a problem that you better understand which is z%5E2-2z-15=0
Now you can factor the problem to factors of 15 that subtract and give you -2 which are -5 and 2
so you get %28z-5%29%28z%2B2%29=0 which means either z-5=0 or z+2=0
so z=5 or z=-2
Substitute 1%2Bsqrt%28x%29 for z and you get:
1%2Bsqrt%28x%29=5 and 1%2Bsqrt%28x%29=-2
sqrt%28x%29=4 and sqrt%28x%29=-3
square both sides and you get
x=16 and x=9
check your answers by plugging in your answers
1. %281%2Bsqrt%2816%29%29%5E2-2%281%2Bsqrt%2816%29%29-15=0
%281%2B4%29%5E2-2%285%29-15=0
25-10-15=0 0=0 so 16 does work!
2.%281%2Bsqrt%289%29%29%5E2-2%281%2Bsqrt%289%29%29-15=0
%281%2B3%29%5E2-2%281%2B3%29-15=0
16-8-15=0 -7 does not equal 0 so 9 does not work. Therefore, your only real answer is x=16
I hope this helps!