How do you solve 2^(x^2+x) - 4^(1+x) = 0?

1 Answer
Aug 9, 2015

Express both terms as powers of 2 and rearrange to get a quadratic in x, giving solutions: x = -1 or x = 2

Explanation:

Add 4^(1+x) to both sides to get:

2^(x^2+x) = 4^(1+x) = (2^2)^(1+x) = 2^(2(1+x)) = 2^(2x+2)

So x^2+x = 2x+2

Subtract 2x+2 from both sides to get:

0 = x^2-x-2 = (x-2)(x+1)

So x = -1 or x = 2