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Question

asked Oct 26, 2024 114k views

2 Answers

Saikou · Answer 1 · 2024-10-28T22:56:52+0000

Answer:

$x=\pm 9\:i$

Explanation:

The given solutions of the quadratic equation 5x² + 405 = 0 are:

$x=\pm \sqrt{(-405)/(5)}$

To simplify the values of x, first divide 405 by 5:

$x=\pm √(-81)$

Rewrite -81 as 9² · -1:

$x=\pm √(9^2 \cdot -1)$

$\textsf{Apply the radical rule:} \quad √(ab)=√(a)√(b)$

$x=\pm √(9^2)√( -1)$

$\textsf{Apply the radical rule:} \quad √(a^2)=a, \quad a \geq 0$

$x=\pm 9√( -1)$

$\textsf{Appl the imaginary number rule:}:\;√(-1)=i$

$\boxed{x=\pm 9\:i}$

Therefore, the equivalent solutions to the given quadratic are x = ±9i.