Finding all complex solutions to this problem

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To solve the equation 4x^4 + 25x^2 + 36 = 0, substituting u = x^2 simplifies the problem to a quadratic equation in terms of u. The quadratic formula can then be applied to find the values of u. It is incorrect to factor out x^2 from the equation since it is not a common term across all parts. After solving for u, the final step involves taking the square root to find the complex solutions for x. This method effectively addresses the problem while ensuring all solutions are found.
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Homework Statement




Find all solutions of the equation.

Homework Equations



4x^4+25x^2+36=0


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{x^2(4x^2+25x+36) }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 x^2?
 
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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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