Find solutions of equation? 14^14x - 2*14^7x + 1=0

This is an exponential equation that
requires substitution technique.

14^14x -
2*14^7x + 1 = 0

It is a bi-quadratic
equation:

We'll substitute 14^7x  by another
variable.

14^7x  = t

We'll
square raise both sides:

14^14x  =
t^2

 We'll re-write the equation, having "t" as
variable.

t^2 - 2t + 1 = 0

The
equation above is the result of expanding the
square:

(t-1)^2 = 0

t1 = t2 =
1

But 14^7x = t1.

14^7x =
1

We'll write 1 as a power of
14:

14^7x= 14^0

Since the
bases are matching, we'll apply the one to one property:

7x
= 0

We'll divide by 7 both
sides:

x =
0.

The solution of the equation is x =
0.