50 Contoh Soal Essay Tentang Menyelesaikan Persamaan Kuadrat

50 Contoh Soal Essay Tentang Menyelesaikan Persamaan Kuadrat Dengan Berbagai Metode – Berikut adalah 50 contoh soal essay tentang menyelesaikan persamaan kuadrat dengan berbagai metode beserta jawabannya, cocok untuk siswa SMP/sederajat dan SMA/sederajat. Metode yang digunakan antara lain: faktorisasi, melengkapkan kuadrat, dan rumus kuadrat.

Metode Faktorisasi

1. Selesaikan: x² – 5x + 6 = 0
Jawaban: (x – 2)(x – 3) = 0 → x = 2 atau x = 3

2. Selesaikan: x² – 7x + 12 = 0
Jawaban: (x – 3)(x – 4) = 0 → x = 3 atau x = 4

3. Selesaikan: x² + 6x + 9 = 0
Jawaban: (x + 3)² = 0 → x = –3

4. Selesaikan: x² – 9 = 0
Jawaban: (x – 3)(x + 3) = 0 → x = 3 atau –3

5. Selesaikan: x² – 2x – 15 = 0
Jawaban: (x – 5)(x + 3) = 0 → x = 5 atau –3

6. Selesaikan: 2x² + 5x – 3 = 0
Jawaban: Faktorisasi → (2x – 1)(x + 3) = 0 → x = ½ atau –3

7. Selesaikan: 3x² – 2x – 1 = 0
Jawaban: (3x + 1)(x – 1) = 0 → x = –⅓ atau 1

8. Selesaikan: x² – 4x = 0
Jawaban: x(x – 4) = 0 → x = 0 atau x = 4

9. Selesaikan: x² + 5x = 0
Jawaban: x(x + 5) = 0 → x = 0 atau x = –5

10. Selesaikan: x² – 16x + 64 = 0
Jawaban: (x – 8)² = 0 → x = 8

11. Selesaikan: 4x² – 25 = 0
Jawaban: (2x – 5)(2x + 5) = 0 → x = 5/2 atau –5/2

12. Selesaikan: x² + 2x – 8 = 0
Jawaban: (x + 4)(x – 2) = 0 → x = –4 atau 2

13. Selesaikan: x² – 10x + 21 = 0
Jawaban: (x – 7)(x – 3) = 0 → x = 7 atau 3

14. Selesaikan: 5x² + 5x = 0
Jawaban: 5x(x + 1) = 0 → x = 0 atau –1

15. Selesaikan: x² – 11x + 24 = 0
Jawaban: (x – 8)(x – 3) = 0 → x = 8 atau 3

16. Selesaikan: x² + 7x + 10 = 0
Jawaban: (x + 2)(x + 5) = 0 → x = –2 atau –5

17. Selesaikan: 6x² – 13x + 6 = 0
Jawaban: (3x – 2)(2x – 3) = 0 → x = ⅔ atau x = 3/2

18. Selesaikan: x² – x – 6 = 0
Jawaban: (x – 3)(x + 2) = 0 → x = 3 atau –2

19. Selesaikan: x² – 49 = 0
Jawaban: (x – 7)(x + 7) = 0 → x = 7 atau –7

20. Selesaikan: x² – 6x = 0
Jawaban: x(x – 6) = 0 → x = 0 atau 6

Metode Melengkapkan Kuadrat

21. Selesaikan: x² + 6x + 5 = 0 dengan melengkapkan kuadrat
Jawaban:
x² + 6x = –5
Tambah 9 → x² + 6x + 9 = 4
(x + 3)² = 4 → x = –3 ± 2 → x = –1 atau –5

22. Selesaikan: x² + 4x + 1 = 0
Jawaban:
x² + 4x = –1
Tambah 4 → x² + 4x + 4 = 3
(x + 2)² = 3 → x = –2 ± √3

23. Selesaikan: x² – 8x + 12 = 0
Jawaban:
x² – 8x = –12
Tambah 16 → x² – 8x + 16 = 4
(x – 4)² = 4 → x = 4 ± 2 → x = 6 atau 2

24. Selesaikan: x² – 2x – 3 = 0
Jawaban:
x² – 2x = 3
Tambah 1 → x² – 2x + 1 = 4
(x – 1)² = 4 → x = 1 ± 2 → x = 3 atau –1

25. Selesaikan: x² + 10x + 21 = 0
Jawaban:
x² + 10x = –21
Tambah 25 → x² + 10x + 25 = 4
(x + 5)² = 4 → x = –5 ± 2 → x = –3 atau –7

26. Selesaikan: x² – 6x + 5 = 0
Jawaban:
x² – 6x = –5
Tambah 9 → x² – 6x + 9 = 4
(x – 3)² = 4 → x = 3 ± 2 → x = 1 atau 5

27. Selesaikan: x² + 2x + 3 = 0
Jawaban:
x² + 2x = –3
Tambah 1 → x² + 2x + 1 = –2
(x + 1)² = –2 → x = –1 ± √(–2) = imajiner

28. Selesaikan: x² – 4x + 2 = 0
Jawaban:
x² – 4x = –2
Tambah 4 → x² – 4x + 4 = 2
(x – 2)² = 2 → x = 2 ± √2

29. Selesaikan: x² + 3x + 2 = 0
Jawaban:
x² + 3x = –2
Tambah 2.25 → x² + 3x + 2.25 = 0.25
(x + 1.5)² = 0.25 → x = –1.5 ± 0.5 → x = –1 atau –2

30. Selesaikan: x² + 8x + 16 = 0
Jawaban: (x + 4)² = 0 → x = –4

31. Selesaikan: x² – 12x + 20 = 0
Jawaban:
x² – 12x = –20
Tambah 36 → (x – 6)² = 16 → x = 6 ± 4 → x = 10 atau 2

32. Selesaikan: x² + x – 6 = 0
Jawaban:
x² + x = 6
Tambah 0.25 → (x + 0.5)² = 6.25 → x = –0.5 ± 2.5 → x = 2 atau –3

33. Selesaikan: x² – 3x + 1 = 0
Jawaban:
x² – 3x = –1
Tambah 2.25 → (x – 1.5)² = 1.25 → x = 1.5 ± √1.25

34. Selesaikan: x² – x – 2 = 0
Jawaban:
x² – x = 2
Tambah 0.25 → (x – 0.5)² = 2.25 → x = 0.5 ± 1.5 → x = –1 atau 2

35. Selesaikan: x² + 5x + 4 = 0
Jawaban:
x² + 5x = –4
Tambah 6.25 → (x + 2.5)² = 2.25 → x = –2.5 ± 1.5 → x = –1 atau –4

Metode Rumus Kuadrat (ABC)

Rumus:

$x = \frac{-b \pm \sqrt{b^2 – 4ac}}{2a}$

x=2a−b±b2−4ac​​​​​​

36. Selesaikan: x² – 4x – 5 = 0
Jawaban:
a = 1, b = –4, c = –5
x = (4 ± √(16 + 20)) / 2 = (4 ± √36)/2 = (4 ± 6)/2 → x = 5 atau –1

37. Selesaikan: x² + 2x – 3 = 0
Jawaban: x = (–2 ± √(4 + 12))/2 = (–2 ± √16)/2 → x = 1 atau –3

38. Selesaikan: 2x² + 3x – 2 = 0
Jawaban: x = (–3 ± √(9 + 16))/4 = (–3 ± √25)/4 → x = ½ atau –2

39. Selesaikan: x² – 6x + 8 = 0
Jawaban: x = (6 ± √(36 – 32))/2 = (6 ± √4)/2 = 4 atau 2

40. Selesaikan: x² + x – 12 = 0
Jawaban: x = (–1 ± √(1 + 48))/2 = (–1 ± √49)/2 = (–1 ± 7)/2 → x = 3 atau –4

41. Selesaikan: x² – x – 1 = 0
Jawaban: x = (1 ± √(1 + 4))/2 = (1 ± √5)/2

42. Selesaikan: 3x² – 5x + 2 = 0
Jawaban: x = (5 ± √(25 – 24))/6 = (5 ± 1)/6 → x = 1 atau 2/3

43. Selesaikan: 4x² – 12x + 9 = 0
Jawaban: x = (12 ± √(144 – 144))/8 = 12/8 = 3/2

44. Selesaikan: x² + 4x + 6 = 0
Jawaban: x = (–4 ± √(16 – 24))/2 = (–4 ± √(–8))/2 → akar imajiner

45. Selesaikan: x² – 10x + 21 = 0
Jawaban: x = (10 ± √(100 – 84))/2 = (10 ± √16)/2 → x = 7 atau 3

46. Selesaikan: x² + 6x + 9 = 0
Jawaban: x = (–6 ± √(36 – 36))/2 = –3

47. Selesaikan: 2x² – x – 3 = 0
Jawaban: x = (1 ± √(1 + 24))/4 = (1 ± √25)/4 → x = 3/2 atau –1

48. Selesaikan: x² + 7x + 10 = 0
Jawaban: x = (–7 ± √(49 – 40))/2 = (–7 ± √9)/2 = –5 atau –2

49. Selesaikan: x² – 2x + 1 = 0
Jawaban: x = (2 ± √(4 – 4))/2 = 2/2 = 1

50. Selesaikan: 5x² – 5x – 10 = 0
Jawaban: x = (5 ± √(25 + 200))/10 = (5 ± √225)/10 → x = 2 atau –1

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