SOLUTION: solve {{{ sqrt(x+3) = x+1 }}} if possible could you include steps on how you reached the answer

Algebra ->  Square-cubic-other-roots -> SOLUTION: solve {{{ sqrt(x+3) = x+1 }}} if possible could you include steps on how you reached the answer      Log On


   

Question 446603: solve +sqrt%28x%2B3%29+=+x%2B1+
if possible could you include steps on how you reached the answer
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
solve sqrt%28x%2B3%29 = x + 1
if possible could you include steps on how you reached the answer
:
Square both sides:
%28sqrt%28x%2B3%29%29%5E2+=+%28x+%2B+1%29%5E2
FOIL the right side
x + 3 = x^2 + 2x + 1
Combine like terms on the right
0 = x^2 + 2x - x + 1 - 3
A quadratic equation
x^2 + x - 2 = 0
Factors to
(x+2)(x-1) = 0
Two solutions
x = -2
and
x = +1
:
:
You must check both solutions in the original equation
x = -2
sqrt%28-2%2B3%29 = -2 + 1
sqrt%281%29 = -1
1 does not = -1, not a valid solition
try x=1
sqrt%281%2B3%29 = 1 + 1
sqrt%284%29 = 2; a good solution