To solve for x in the equation 10^x^2 + x - 2 = 1, we first need to simplify the equation by moving the 1 to the left side:

10^x^2 + x - 2 - 1 = 0
10^x^2 + x - 3 = 0

Now we need to find the values of x that satisfy this equation. This is a quadratic equation in terms of x, so we can use the quadratic formula to find the solutions:

x = (-b ± √(b^2 - 4ac)) / 2a

In this case, a = 10, b = 1, and c = -3. Plugging these values into the formula:

x = (-(1) ± √((1)^2 - 4(10)(-3))) / 2(10)
x = (-1 ± √(1 + 120)) / 20
x = (-1 ± √121) / 20
x = (-1 ± 11) / 20

This gives us two possible solutions for x:

x = (11 - 1) / 20 = 10 / 20 = 0.5
or
x = (-1 - 11) / 20 = -12 / 20 = -0.6

Therefore, the solutions to the equation 10^x^2 + x - 2 = 1 are x = 0.5 and x = -0.6.