Tentukan akar persamaan kuadrat berikut dengan melengkapkan kuadrat sempurna1. X² + 4X + 3 = 0
2. X² - 6X + 8 = 0
3. 2X² + 4X + 6 = 0
4. X² - 5X - 14 = 0
5. X² + 3X = 18​

Jawaban :
1. X^2 + 4X + 3 = 0
X^2 + 4X = -3
X^2 + 4X + (4/2)^2 = -3 + (4/2)^2
(X + 4/2)^2 = -3 + 16/4
(X + 4/2)^2 = -12/4 + 16/4
(X + 4/2)^2 = 4/4 = 1

X + 4/2 = + 1
X = 1 - 4/2
X = 2/2 - 4/2
X = 2/2 = 1
dan
X = - 1 - 4/2
X = 2/2 - 4/2
X = -6/2 = 2

2. X^2 - 6X + 8 = 0
X^2 - 6X = - 8
X^2 - 6X - (6/2)^2 = -8 - (6/2)^2
(X - 6/2)^2 = -8 - 9
(X - 6/2)^2 = -17
X - 6/2 = +- 4

X - 6/2 = + 4
X = 4 + 6/2
X = 8/2 + 6/2 = 14/2 = 7

dan

X - 6/2 = -4
X = -4 + 6/2
X = -8/2 + 6/2 = -2/2 = -1

3. 2X^2 + 4X + 6 = 0 dibagi dngn 2 karena koef X^2 harus menjadi 1
X^2 + 2X + 3 = 0
X^2 + 2X = -3
X^2 + 2X + (2/2)^2 = -3 + (2/2)^2
(X + 2/2)^2 = -12/4 + 4/4
(X + 2/2)^2 = -8/4 = -2
X + 2/2 = +- 2

X = + 2 - 2/2
X = 4/2 - 2/2 = 2/2 = 1

dan

X = -2 - 2/2
X = -4/2 - 2/2 = -6/2 = -3

4. X^2 - 5X - 14 = 0
X^2 - 5X = 14
X^2 - 5X - (5/2)^2 = 14 - (5/2)^2
(X - 5/2)^2 = 14 - 25/4
(X - 5/2)^2 = 56/4 - 25/4 = 31/4
(X - 5/2)^2 = 2,7 = 3
X - 5/2 = +- 5

X = 5 + 5/2
X = 10/2 + 5/2 = 15/2

dan

X = -5 + 5/2
X = -10/2 + 5/2 = -5/2

maaf jika salah