To solve this equation, we first need to expand and simplify both terms on the left side:
Expand (x^-4)^2:(x^-4)^2 = x^-8 = 1/x^8
Expand (x^2-3x-10)^2:(x^2-3x-10)^2 = (x^2-3x-10)(x^2-3x-10)= x^4 - 3x^3 - 10x^2 - 3x^3 + 9x^2 + 30x - 10x^2 + 30x + 100= x^4 - 6x^3 + 29x^2 + 60x + 100
Now, the equation becomes:1/x^8 + x^4 - 6x^3 + 29x^2 + 60x + 100 = 0
This is a quintic equation (degree 5) and it can be quite challenging to solve algebraically. You may need to use numerical methods or a graphing calculator to find the solutions.
To solve this equation, we first need to expand and simplify both terms on the left side:
Expand (x^-4)^2:
(x^-4)^2 = x^-8 = 1/x^8
Expand (x^2-3x-10)^2:
(x^2-3x-10)^2 = (x^2-3x-10)(x^2-3x-10)
= x^4 - 3x^3 - 10x^2 - 3x^3 + 9x^2 + 30x - 10x^2 + 30x + 100
= x^4 - 6x^3 + 29x^2 + 60x + 100
Now, the equation becomes:
1/x^8 + x^4 - 6x^3 + 29x^2 + 60x + 100 = 0
This is a quintic equation (degree 5) and it can be quite challenging to solve algebraically. You may need to use numerical methods or a graphing calculator to find the solutions.