Question

Hello,
I've been having trouble with the following question:
Identify all real solutions for x in the equation 2(2^x- 1) x^2 + (2^{x^2}-2)x = 2^{x+1} -2.
Please help ASAP.
Thanks in advance!

Answer 1

well, just by inspection, x=0 works, since you have
0 + 0 = 2-2
Also, trying for low-hanging fruit, x=1 works, since
2(2-1)*1 + 0 = 4-2
Also, x = -1 works, since
2(1/2 - 1) + 0 = 1-2

But I'm still struggling on an algebraic solution.

Answer 2

Thanks for the response. I also got the solutions of 0 and 1 just by guess and check but I have no idea how it works!

Answer 3

I found out how to solve it! You can factor the right side of the equation and subtract that from both sides, then factor by grouping the left side of the equation, which gives x = -1, 0, and 1.