Let's first simplify the equation:

(2x^2 - 10)^2 + 2(2x^2 - 10) + 1 = 0

Expanding the square of the binomial:

(4x^4 - 40x^2 + 100) + 4x^2 - 20 + 1 = 0

Combine like terms:

4x^4 - 36x^2 + 81 = 0

Now, we have a quadratic equation in terms of x^2:

Let y = x^2. The equation becomes:

4y^2 - 36y + 81 = 0

Now, we can solve for y using the quadratic formula:

y = [ -(-36) ± √((-36)^2 - 4481) ] / 2*4

y = [ 36 ± √(1296 - 1296) ] / 8

y = 4

Since y = x^2, we have:

x^2 = 4

Taking the square root of both sides:

x = ±2

Therefore, the solutions to the equation are x = 2 and x = -2.