Finding all complex solutions to this problem

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SUMMARY

The discussion focuses on solving the equation 4x^4 + 25x^2 + 36 = 0. Participants clarify that factoring out x^2 is not possible due to the absence of x^2 in all terms. Instead, the recommended approach is to substitute u = x^2, transforming the equation into a standard quadratic form, which can then be solved using the quadratic formula. This method leads to finding the values of u, which can subsequently be used to determine the solutions for x.

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Homework Statement




Find all solutions of the equation.

Homework Equations



[tex]4x^4+25x^2+36=0[/tex]


The Attempt at a Solution



Where do i start here? do i use the quadratic formula? I'm thinking i can factor out a x^2 to make it{[tex]x^2(4x^2+25x+36)[/tex] }and from there i can do the quadratic formula. Another question: can i not factor out x^2 since it is not common to all terms because 36 has no [tex]x^2?[/tex]
 
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No, you can't factor x^2 out. You can, on the other hand, substitute u=x^2, solve for u using the quadratic equation and then find x.
 

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