If: x2-4 = 0 Then: x = 2
x2 - 4x + 4 = 0 (x - 2)(x - 2) = 0 x = 2
-x2 = x - 6 x2 + x - 6 = 0 (x - 2)(x + 3) = 0 x ∈ {-3, 2}
x2 - x - 6 = (x - 3)(x + 2) = 0; whence, x = 3 or -2.
x2 + 3x + 7 = 5 ∴ x2 + 3x + 2 = 0 ∴ (x + 1)(x + 2) = 0 ∴ x ∈ {-2, -1}
If: x2-4 = 0 Then: x = 2
x2 - 3x + 2 = 0
x2 - 4x + 4 = 0 (x - 2)(x - 2) = 0 x = 2
-x2 = x - 6 x2 + x - 6 = 0 (x - 2)(x + 3) = 0 x ∈ {-3, 2}
x2 - x - 6 = (x - 3)(x + 2) = 0; whence, x = 3 or -2.
x = √(2-x) x2 = 2-x x2 + x = 2 x2 + x - 2 = 0 (x+2)(x-1) = 0 x = 1 or -2
x2 + 3x + 7 = 5 ∴ x2 + 3x + 2 = 0 ∴ (x + 1)(x + 2) = 0 ∴ x ∈ {-2, -1}
-2
2x = x2 + 4x - 3 x2 + 2x - 3 = 0 (x - 1)(x - 2) = 0
x2 - 14x = -49 ∴ x2 - 14x + 49 = 0 ∴ (x - 7)2 = 0 ∴ x = 7
x2 + 6x - 2 = 0 x2 + 6x + 9 = 13 (x + 3)2 = 13 x + 3 = ± √13 x = -3 ± √13
x = 2 or -2