Item 1
[tex] {x}^{2} = 2x \\ {x}^{2} - 2x = 0 \\ x(x - 2) = 0 [/tex]
Meaning, x = 0 and x = 2.
Item 2
[tex]x(x + 1) = 12 \\ {x}^{2} + x - 12 = 0 \\ (x + 4)(x - 3) = 0 [/tex]
Meaning, x = -4 and x = 3.
Item 3
[tex]x(x + 1) = 42 \\ {x}^{2} + x - 42 = 0 \\ (x + 7)(x - 6) = 0[/tex]
Meaning, x = -7 and x = 6.
Item 4
[tex](x - 3)(x + 3) = 40 \\ {x}^{2} - 9 = 40 \\ {x}^{2} - 49 = 0 \\ (x + 7)(x - 7) = 0[/tex]
Meaning, x = ±7.
Item 5
[tex]9 {x}^{2} - 4 = 0 \\ (3x + 2)(3x - 2) = 0[/tex]
Meaning, x = ± 2/3.
Hope this helps.
