SOLUTION: Solve the equation. Show work. sqrt 2x + 5 - sqrt x-2 = 3

Algebra ->  Square-cubic-other-roots -> SOLUTION: Solve the equation. Show work. sqrt 2x + 5 - sqrt x-2 = 3      Log On


   

Question 83949: Solve the equation. Show work.
sqrt 2x + 5 - sqrt x-2 = 3
Answer by Nate(3500) About Me  (Show Source):
You can put this solution on YOUR website!
sqrt%282x+%2B+5%29+-+sqrt%28x+-+2%29+=+3
.
sqrt%282x+%2B+5%29+=+3+%2B+sqrt%28x+-+2%29
.
sqrt%282x+%2B+5%29%5E2+=+%283+%2B+sqrt%28x+-+2%29%29%5E2
.
2x+%2B+5+=+9+%2B+6%2Asqrt%28x+-+2%29+%2B+x+-+2
.
x+-+2+=+6%2Asqrt%28x+-+2%29
.
%28x+-+2%29%2F6+=+sqrt%28x+-+2%29
.
%28%28x+-+2%29%2F6%29%5E2+=+sqrt%28x+-+2%29%5E2
.
%28x%5E2+-+4x+%2B+4%29%2F36+=+x+-+2
.
x%5E2+-+4x+%2B+4+=+36x+-+72
.
x%5E2+-+40x+%2B+76+=+0
.
%28x+-+38%29%28x+-+2%29+=+0
.
x+=+38 and x+=+2 ~ After checking, they both work....