1. We are asked to solve an equation using substitution. 2. The substitution method involves replacing a complicated expression with a simpler variable to make the equation easier to solve. 3. Suppose the original equation is of the form $$ax^2 + bx + c = 0$$ or involves expressions like $$x^4$$ or $$\sqrt{x}$$, we choose a substitution such as $$u = x^2$$ or $$u = \sqrt{x}$$. 4. After substitution, solve the simpler equation in terms of $$u$$. 5. Once $$u$$ is found, substitute back to find $$x$$. 6. Example: Solve $$x^4 - 5x^2 + 6 = 0$$ using substitution. 7. Let $$u = x^2$$, then the equation becomes $$u^2 - 5u + 6 = 0$$. 8. Factor the quadratic: $$(u - 2)(u - 3) = 0$$. 9. So, $$u = 2$$ or $$u = 3$$. 10. Substitute back: $$x^2 = 2$$ or $$x^2 = 3$$. 11. Solve for $$x$$: $$x = \pm \sqrt{2}$$ or $$x = \pm \sqrt{3}$$. 12. Final solutions are $$x = \pm \sqrt{2}, \pm \sqrt{3}$$. This method simplifies solving complex equations by reducing their degree or complexity through substitution.