How do you factor the equation with negative exponents: \(-4x^{-4} - 3x^{-2} + 1 = 0\)?

Please show all steps. Thank you.

− 4 x − 4 − 3 x − 2 + 1 = 0 − 4 x − 4 − 4 x − 2 + x − 2 + 1 = 0 − 4 x − 2 ( x − 2 + 1 ) + 1 ( x − 2 + 1 ) = 0 − ( 4 x − 2 − 1 ) ( x − 2 + 1 ) = 0 4 x − 2 − 1 = 0 ∨ x − 2 + 1 = 0 4 x − 2 = 1 ∨ x − 2 = − 1 x − 2 = 4 1 ​ ∨ x 2 1 ​ = − 1 x 2 1 ​ = 4 1 ​ x = − 2 ∨ x = 2

Answered by konrad509 | 2024-06-10

To factor the equation − 4 x − 4 − 3 x − 2 + 1 = 0 , we substitute y = x − 2 and rewrite it as a quadratic equation. Factoring leads to the solutions x = 1 and x = − 1 .
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Answered by konrad509 | 2024-12-26