Solve for x x^4-20x^2+64=0

Problem

x4−20*x2+64=0

Solution

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

u2−20*u+64=0

2. Factor the quadratic equation by finding two numbers that multiply to 64 and add to −20 These numbers are −4 and −16

(u−4)*(u−16)=0

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

u=4

u=16

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

x2=4

x2=16

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

x=±√(,4)

x=±√(,16)

x=±2

x=±4

Final Answer

x={−4,−2,2,4}

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