SOLUTION: I am having trouble solving this equation for x. Could you help me? Thanks! 2e^x + 4xe^x + (x^2-1)e^x = 0

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Question 691174: I am having trouble solving this equation for x. Could you help me? Thanks!
2e^x + 4xe^x + (x^2-1)e^x = 0
Found 2 solutions by pmatei, MathLover1:
Answer by pmatei(79) About Me  (Show Source):
You can put this solution on YOUR website!
Factor e%5Ex:
%28e%5Ex%29%282%2B4x%2Bx%5E2-1%29=0
%28e%5Ex%29%28x%5E2%2B4x%2B1%29=0
e%5Ex is not zero ever, so:
x%5E2%2B4x%2B1=0
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
2e%5Ex+%2B+4xe%5Ex+%2B+%28x%5E2-1%29e%5Ex+=+0....first multiply %28x%5E2-1%29e%5Ex
2e%5Ex+%2B+4xe%5Ex+%2B+x%5E2e%5Ex-1e%5Ex=+0
x%5E2e%5Ex+%2B+4xe%5Ex+%2Be%5Ex=+0
e%5Ex%2Ax%5E2+%2B+4e%5Ex%2Ax+%2Be%5Ex=+0....here you have a quadratic equation (in general form ax%5E2%2Bbx%2Bc=0), where a=e%5Ex, b=4e%5Ex and c=e%5Ex
now you use quadratic formula to solve for x

x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+ ....plug in values for a, b and c

x+=+%28-4e%5Ex+%2B-+sqrt%28%284e%5Ex%29%5E2-4%2Ae%5Ex%2Ae%5Ex+%29%29%2F%282%2Ae%5Ex%29+

x+=+%28-4e%5Ex+%2B-+sqrt%2816e%5E%282x%29-4%2Ae%5E%282x%29+%29%29%2F%282e%5Ex%29+

x+=+%28-4e%5Ex+%2B-+sqrt%2812e%5E%282x%29+%29%29%2F%282e%5Ex%29+....since e%5E%282x%29=%28e%5Ex%29%5E2, we will have

x+=+%28-4e%5Ex+%2B-+sqrt%284%2A3%28e%5Ex%29%5E2+%29%29%2F%282e%5Ex%29+

x+=+%28-4e%5Ex+%2B-+2%28e%5Ex%29sqrt%283+%29%29%2F%282e%5Ex%29+.......factor out %281%2F2%29

.....cancel %28e%5Ex%29

x+=+%281%2F2%29%28-4+%2B-+2sqrt%283+%29%29+
solutions:
x+=+%281%2F2%29%28-4+%2B+2sqrt%283+%29%29+

x+=+%281%2F2%29%28-4+%2B+2%2A1.73%29+

x+=+%281%2F2%29%28-4+%2B+3.46%29+

x+=+%281%2F2%29%28-0.54%29+
x+=-0.27............if you plug in x+=-0.27 in given equation, you will get answer -0.00541999 which is rounded to whole number equal to zero
or
x+=+%281%2F2%29%28-4+-2sqrt%283+%29%29+

x+=+%281%2F2%29%28-4-2%2A1.73%29+

x+=+%281%2F2%29%28-4+-+3.46%29+

x+=+%281%2F2%29%28-7.46%29+

x+=-3.73...........if you plug in x+=-3.73, you get -0.000170349, you also round it to zero
the difference appears because rounding decimals during calculation of x