Solve for x x^4-13x^2+36=0

Problem

x4−13*x2+36=0

Solution

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

u2−13*u+36=0

2. Factor the quadratic equation by finding two numbers that multiply to 36 and add to −13 These numbers are −4 and −9

(u−4)*(u−9)=0

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

u=4

u=9

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

x2=4

x2=9

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

x=±√(,4)

x=±√(,9)

Final Answer

x={−3,−2,2,3}

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