X² - 5 = ( x - 5)(2x - 1)
x² - 5 = 2x² - x - 10x + 5
x² - 2x² + x + 10x = 5 + 5
- x² + 11x - 10 = 0
x² - 11x + 10 = 0
D = b² - 4ac = ( - 11)² - 4 × 1 × 10 = 121 - 40 = 81 = 9²
x₁ = 11 + 9 / 2 = 10
x₂ = 11 -9 / 2 = 1
( 3x - 1)² = 1
( 3x - 1)( 3x - 1) = 1
9x² - 3x - 3x + 1 - 1 = 0
9x² - 6x + 0 = 0
D = b² - 4ac = 36 - 4 × 9 × 0 = 36 = 6²
x₁ = 6 + 6 / 18 = 12/18 = 6/9 = 2/3
x₂ = 6 - 6 / 18 = 0
( x + 3)( x - 4) = -12
x² - 4x + 3x - 12 = - 12
x² - x - 12 + 12 = 0
x² - x + 0 = 0
D = b² - 4ac = 1 - 4 × 1 × 0 = 1 = 1²
x₁ = 1 + 1 / 2 = 1
x₂ = 1 - 1 / 2 = 0
( 3x - 1)² = 4 - 12x
(3x - 1)( 3x - 1) = 4 - 12x
9x² - 3x - 3x + 1 = 4 - 12x
9x² - 6x + 1 - 4 + 12x = 0
9x² + 6x - 3 = 0
D = b² - 4ac = 36 - 4 × 9 × ( - 3) = 36 + 108 = 144 = 12²
x₁ = - 6 + 12 / 18 = 6 / 18 = 1/3
x₂ = - 6 - 12 / 18 = - 18 / 18 = - 1