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

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Answer 1 · 2015-10-25T15:00:09

$x=1$

First, rearrange the equation like this:

$2^(2x) + 2^(x + 2) - 12 = 0$

$(2^x)^2 + 4(2^x) - 12 = 0$

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

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

$(s+6)(s-2)=0$

$s=-6$ 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

How do you solve 2^(2x) + 2^(x + 2) - 12 = 02^(2x) + 2^(x + 2) - 12 = 0?