Solve for x x^4-17x^2+16=0

Problem

x4−17*x2+16=0

Solution

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

u2−17*u+16=0

2. Factor the quadratic equation by finding two numbers that multiply to 16 and add to −17

(u−16)*(u−1)=0

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

u=16

u=1

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

x2=16

x2=1

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

x=±4

x=±1

Final Answer

x={−4,−1,1,4}

Want more problems? Check here!