Find all solutions of the equation 2^(x^2-5x+10)-64=0

We'll shift the number alone to the right
side:

2^(x^2-5x+10) = 64

We'll
create matching bases both sides. For this reason, we'll re-write 64 =
2^6

We'll re-write the equation as it
follows:

2^(x^2-5x+10)=
2^6

Since the bases are matching now, we'll apply one to
one rule and we'll
get:

(x^2-5x+10)=6

We'll
subtract 6 both
sides:

x^2-5x+10-6=0

x^2-5x+4=0

We'll
apply quadratic
formula:

x1=[5+sqrt(25-16)]/2

x1=(5+3)/2

x1=4

x2=(5-3)/2

x2=1

The
complete set of solutions of the exponential equation is: {1 ;
4}.