# How do you solve 2^(2x) + 2^(x + 2) - 12 = 0?

Oct 25, 2015

$x = 1$

#### Explanation:

First, rearrange the equation like this:

${2}^{2 x} + {2}^{x + 2} - 12 = 0$

${\left({2}^{x}\right)}^{2} + 4 \left({2}^{x}\right) - 12 = 0$

Now, treat this like a quadratic equation by substituting ${2}^{x} = s$:

${s}^{2} + 4 s - 12 = 0$

$\left(s + 6\right) \left(s - 2\right) = 0$

$s = - 6$ or $s = 2$

Now, go back to the substitution:

${2}^{x} = s$

${2}^{x} = - 6$ or ${2}^{x} = 2$

Since ${2}^{x}$ can never equal a negative number, we can rule out the first solution.

However, the second solution results in $x = 1$

Hope that helped