Solve the equation 10^(1+x^2) - 10^(1-x^2)=99

We'll re-write the
equation:

10*10^(x^2) - 10/10^(x^2) - 99 =
0

We'll replace 10^(x^2) by
t:

10*t - 10/t - 99 = 0

10t^2
- 99t - 10 = 0

We'll apply quadratic
formula:

t1 =
[99+sqrt(9801+400)]/20

t1 =
(99+101)/20

t1 = 10

t2 =
(99-101)/20

t2 = -0.1

But
10^(x^2) = t1 <=> 10^(x^2) = 10

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

x^2 = 1
<=> x1 = -1 and x2 = 1

10^(x^2) = t1
<=> 10^(x^2) =-0.1 ,
impossible.

The possible solutions of the
equation are: {-1 ; 1}.