2x+x⁹=

To solve the equation 2x + x⁹ = 0, we need to isolate x.

First, let's rearrange the equation by bringing all the x terms to one side:

x⁹ + 2x = 0

Now, we can factor out x from both terms:

x(x⁸ + 2) = 0

To find the solutions, set each factor equal to zero:

x = 0 x⁸ + 2 = 0

For x⁸ + 2 = 0, we can use the difference of squares factorization:

(x⁴ + √2)(x⁴ - √2) = 0

Setting each factor equal to zero, we have:

x⁴ + √2 = 0 x⁴ - √2 = 0

Taking the square root of both sides gives:

x⁴ = -√2 x⁴ = √2

Since we are solving for x, taking the fourth root of both sides gives:

x = (-√2)^(1/4) x = √2^(1/4)

The exact solutions of the equation 2x + x⁹ = 0 are:

x = 0, x = (-√2)^(1/4), x = √2^(1/4)