SOLUTION: Find all solutions. x^2 + x - 2 + square root of (x^2 + x) = 0

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Question 322154: Find all solutions. x^2 + x - 2 + square root of (x^2 + x) = 0
Answer by Jk22(389) About Me  (Show Source):
You can put this solution on YOUR website!
x%5E2+%2B+x+-+2+%2B+sqrt%28x%5E2+%2B+x%29=0
=%28x%2B2%29%28x-1%29%2Bsqrt%28x%28x%2B1%29%29
=>%28x%2B2%29%28x-1%29=-sqrt%28x%28x%2B1%29%29--->domains : x in [-2;1]^]-1;0[=[-2;-1]U[0;1]
symmetry : let x=y-1/2 :
%28y%2B3%2F2%29%28y-3%2F2%29=-sqrt%28%28y-1%2F2%29%28y%2B1%2F2%29%29 | square
%28y%5E2-9%2F4%29%5E2=%28y%5E2-1%2F4%29
y%5E4-%289%2F2%29%2Ay%5E2%2B81%2F16=y%5E2-1%2F4
y%5E4-%2811%2F2%29%2Ay%5E2%2B85%2F16=0
=> y^2=(11+-6)/4=17/4 or 5/4
solution in domain : x=%28%2B-+sqrt%285%29-1%29%2F2