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- 1 decade agoFavorite Answer
要解 Completing Square，先要知道 Perfect Square

Perfect Square:

(a + b)² = a² + 2ab + b²

方程：

x² - 5x + 6 = 0

(x² - 5x + ( 5 / 2(1) )² ) + 6 - ( 5 / 2(1) )² = 0

(x - 5 / 2)² - 1 / 4 = 0

x - 5 / 2 = ±1 / 2

x = (5 ± 1) /2 = 3 or 2

x² + 7x - 5 = 0

(x² + 7x + ( 7 / 2(1) )² ) - 5 - ( 7 / 2(1) )² = 0

(x + 7 / 2)² - 69 / 4 = 0

x + 7 / 2 = ±√69 / 2

x = (-7 ±√69) / 2

- ?Lv 51 decade ago
Completing Square 即係將 有 2 次方既 方程式 「整」到 佢 變成 (X + ?)² 咁款！跟住求答案！

e.g. Solve x² + 6x – 7 = 0 by completing the square

x² + 6x = 7

因為我地知道 x² + 6x + 9 = (x + 3)²

所以我地「砌」個 "+ 9" 入去

x² + 6x + 9 = 7 + 9

(x + 3)² = 16

(x + 3)² = 4²

所以 (x + 3) = +4 或者 -4

x + 3 = 4 或者 x + 3 = -4

x = 1 或者 x = -7

上述既方法就叫做 “Completing square ”

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