SOLUTION: solve for x: x=(square root of 2x+1) plus 1

Algebra ->  Radicals -> SOLUTION: solve for x: x=(square root of 2x+1) plus 1      Log On


   

Question 295822: solve for x: x=(square root of 2x+1) plus 1
Answer by alicealc(293) About Me  (Show Source):
You can put this solution on YOUR website!
x+=+sqrt%282x+%2B+1%29+%2B+1
x+-+1+=+sqrt%282x+%2B+1%29
%28x+-+1%29%5E2+=+%28sqrt%282x+%2B+1%29%29%5E2
x%5E2+-+2x+%2B+1+=+2x+%2B+1
x%5E2+-+2x+%2B+1+-+2x+-+1+=+0
x%5E2+-+4x+=+0
x%2A%28x+-+4%29+=+0
x = 0 or x - 4 = 0
x = 0 or x = 4

let's check the answer:
if x = 0 then
0+=+sqrt%282%2A0%2B1%29%2B1
0+=+sqrt%280%2B1%29%2B1
0+=+sqrt%281%29%2B1
0+=+1%2B1
0+=+2
because the left and the right side aren't match, so we won't use this answer
if x = 4 then
4+=+sqrt%282%2A4%2B1%29%2B1
4+=+sqrt%288%2B1%29%2B1
4+=+sqrt%289%29%2B1
4+=+3%2B1
4+=+4
the left side and the right side are match, so the answer is: x = 4