① （1 / 2）（x + 1）² - 4 = 0
x ² + 2 x + 1 - 4 = 0
x ² + 2 x - 3 = 0
a = 1 ,b = 2 ,c = - 3
∵ △ = b ² - 4 a c
= 2 ² - 4 × 1 × （- 3）
= 4 + 4 × 3
= 4 + 12
= 16 > 0
∴ 此方程有两个不等实数根.
∴ x = 【 - b ± √（b ² - 4 a c）】 / 2 a
= 【 - 2 ± √ 16 】 / 2 × 1
= （- 2 ± 4）/ 2
= - 1 ± 2
x1 = - 1 + 2 = 1
x2 = - 1 - 2 = - 3
② x ² - 2 x - 4 = 0
x ² - 2 x + 1 = 4 + 1
（x + 1）² = 5
x + 1 = ±√5
x = ±√5 - 1
x1 = √5 - 1
x2 = - √5 - 1
③ （x - 1）（x + 4）= 6
x ² + 3 x - 4 = 6
x ² + 3 x - 10 = 0
（x + 5）（x - 2）= 0
x + 5 = 0 或 x - 2 = 0
x1 = - 5 x2 = 2
④ （x + 1）² - 4 = 0
（x + 1 + 4）（x + 1 - 4）= 0
（x + 5）（x - 3）= 0
x + 5 = 0 或 x - 3 = 0
x1 = - 5 x2 = 3
⑤ （x - 3）² - 2 x（x - 3）= 0
（x - 3）（x - 3 - 2 x）= 0
（x - 3）（- x - 3）= 0
-（x - 3）（x + 3）= 0
x - 3 = 0 或 x + 3 = 0
x1 = 3 x2 = - 3
⑥ （1 / 2）（x + 1）² - 4 = 0
（x + 1）² = 4
x + 1 = ± 2
x = ± 2 - 1
x1 = 2 - 1 = 1
x2 = - 2 - 1 = - 3
⑦ 方程与 ③ 重复.