Solve for x x^4-6x^2+5=0

Problem

x4−6*x2+5=0

Solution

1. Substitute a new variable to transform the equation into a quadratic form. Let u=x2

u2−6*u+5=0

2. Factor the quadratic equation by finding two numbers that multiply to 5 and add to −6

(u−5)*(u−1)=0

3. Solve for u by setting each factor equal to zero.

u=5

u=1

4. Back-substitute x2 for u to find the values of x

x2=5

x2=1

5. Extract the square roots to find all possible solutions for x

x=±√(,5)

x=±1

Final Answer

x=±√(,5),±1

Want more problems? Check here!