# How do you solve 4^(2x) + 4^x + 12 = 0?

Aug 5, 2015

There is no real solution.

#### Explanation:

${4}^{2 x} + {4}^{x} + 12 = 0$

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

You can do a replacement: $u = {4}^{x}$

${u}^{2} + u + 12 = 0$

$u = \frac{- 1 \pm \sqrt{{1}^{2} - 4 \left(1\right) \left(12\right)}}{2}$

$= \frac{- 1 \pm \sqrt{- 47}}{2}$

$u$ is imaginary so we would need ${4}^{x}$ is imaginary and whie that is certainly possible for imaginary $x$, it is not normally handled in a precalculus study of mathematics.

There is no real solution.