SOLUTION: {{{ sqrt (50 + 7k) }}} = (k + 8) I am supposed to figure out what the variable is. So far, I have squared both sides so the "50 + 7k" is no longer a square root. and the k is sq

Algebra ->  Rational-functions -> SOLUTION: {{{ sqrt (50 + 7k) }}} = (k + 8) I am supposed to figure out what the variable is. So far, I have squared both sides so the "50 + 7k" is no longer a square root. and the k is sq      Log On


   

Question 77196This question is from textbook
: +sqrt+%2850+%2B+7k%29+ = (k + 8)
I am supposed to figure out what the variable is. So far, I have squared both sides so the "50 + 7k" is no longer a square root. and the k is squared and 8 is now 64. From there, I subtracted 50 from both sides, but then I got to a place where I had to find the square root of "7k" and then i got totally lost. Would you be able to help me? Thank you. This question is from textbook

Found 2 solutions by avidreader27, tutorcecilia:
Answer by avidreader27(9) About Me  (Show Source):
You can put this solution on YOUR website!
The first problem occured when you tried to square (k+8). The answer would not be K^2 and 64. The square that, you need to multiply like this:
(k+8)(k+8) which gives: k^2+16k+64.
You then have:
50+7k = k^2+16k=64
move the 50 and 7k to the other side:
k^2+9k+14=0
then you factor this equation:
(k+7)(k+2)
setting each of these = to 0 to solve for k you get:
k+7=0 and k+2=0
k= -7 or -2 <---- answer
Hope this helps!!!

Answer by tutorcecilia(2152) About Me  (Show Source):
You can put this solution on YOUR website!
%28+sqrt%2850%2B7k%29+%29=%28x%2B8%29
%28+%28sqrt%2850%2B7k%29%29%5E2+%29=%28x%2B8%29%5E2 [square both sides]
%28+%2850%2B7k%29+%29=%28k%2B8%29%28k%2B8%29
%28+%2850%2B7k%29+%29=%28k%5E2%2B16k%2B64%29%29
%28+0%29=%28k%5E2%2B16k-7k%2B64-50%29%29
%28+0%29=%28k%5E2%2B9k%2B14%29%29
0=(k+7)(k+2)
k+7=0
k=-7
or
k+2=0
k=-2
.
check by plugging k=-7 and k=-2 back into the orignal equation and solve for each value.