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

Problem

x4−5*x2−4=0

Solution

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

u2−5*u−4=0

2. Apply the quadratic formula to solve for u where a=1 b=−5 and c=−4

u=(−(−5)±√(,(−5)2−4*(1)*(−4)))/(2*(1))

3. Simplify the expression under the radical and solve for u

u=(5±√(,25+16))/2

u=(5±√(,41))/2

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

x2=(5±√(,41))/2

5. Solve for x by taking the square root of both sides for both possible values of u

x=±√(,(5±√(,41))/2)

Final Answer

x=±√(,(5+√(,41))/2),±√(,(5−√(,41))/2)

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