[tex]a)\\x(x^{2}-25) = 0\\\\x(x+5)(x-5) = 0\\\\x = 0 \ \vee \ x+5 = 0 \ \vee \ x-5 = 0\\\\x = 0 \ \vee \ x = -5 \ \vee \ x = 5\\\\x \in \{-5, 0, 5\}\\[/tex]
[tex]b)\\x(4x^{2}-1) = 0\\\\x(2x+1)(2x-1) = 0\\\\x = 0 \ \vee \ 2x+1 = 0 \ \vee \ 2x-1 = 0\\\\x = 0 \ \vee \ 2x = -1 \ \vee \ 2x=1\\\\x = 0 \ \vee \ x = -\frac{1}{2} \ \vee \ x = \frac{1}{2}\\\\x \in \{-\frac{1}{2}, 0,\frac{1}{2}\}[/tex]
[tex]c)\\x(9x^{2}-4) = 0\\\\x(3x+2)(3x-2) = 0\\\\x = 0 \ \vee \ 3x+2 = 0 \ \vee \ 3x-2 = 0\\\\x = 0 \ \vee \ 3x = -2 \ \vee \ 3x = 2\\\\x = 0 \ \vee \ x = -\frac{2}{3} \ \vee \ x = \frac{2}{3}\\\\x \in \{-\frac{2}{3}, 0, \frac{2}{3}\}[/tex]
[tex]d)\\x(x^{2}-6x+9) = 0\\\\x(x-3)^{2} = 0\\\\x(x-3) = 0\\\\x = 0 \ \vee \ x-3 = 0\\\\x = 0 \ \vee \ x = 3\\\\x \in \{0,3\}[/tex]
[tex]e)\\x(4x^{2}+4x+1)=0\\\\x(2x+1)^{2} = 0\\\\x(2x+1) = 0\\\\x = 0 \ \vee \ 2x+1 = 0\\\\x = 0 \ \vee \ 2x = -1 \ \ /:2\\\\x = 0 \ \vee \ x = -\frac{1}{2}\\\\x \in \{-\frac{1}{2}, 0\}[/tex]
[tex]f)\\x(x^{2}-x+\frac{1}{4}) = 0\\\\x(x-\frac{1}{2})^{2} = 0\\\\x(x-\frac{1}{2}) = 0\\\\x = 0 \ \vee \ x-\frac{1}{2} = 0\\\\x = 0 \ \vee \ x = \frac{1}{2}\\\\x \in \{0, \frac{1}{2}\}[/tex]
