Answer:
1. x = ±2√2
2. x1 = 0 , x2 = 4
3. x1 = 0 , x2 = 14
4. x1 = 0 , x2 = 3
5. x1 = 0 , x2 = 15/7
Step-by-step explanation:
I.
1. x² - 8 = 0
x² = 8
√x² = √8
x = ±√2² × 2
x = ±2√2
2. 5x² - 20x = 0
5x² ÷ 5 - 20x ÷ 5 = 0 ÷ 5
x² - 4x = 0
x² - 4x + 4 = 0 + 4
(x - 2)² = 4
√(x - 2)² = √4
x - 2 = ±2
x - 2 = 2
x = 2 + 2
x = 4
x - 2 = - 2
x = -2 + 2
x = 0
3. x² = 14x
x² - 14x = 0
x² - 14x + 49 = 0 + 49
(x - 7)² = 49
√(x - 7)² = √49
x - 7 = ±7
x - 7 = 7
x = 7 + 7
x = 14
x - 7 = -7
x = -7 + 7
x = 0
4. 9x² - 27x = 0
9x² ÷ 9 - 27x ÷ 9 = 0 ÷ 9
x² - 3x = 0
x² - 3x + 9/4 = 0 + 9/4
(x - 3/2)² = 9/4
√(x - 3/2)² = √9/4
x - 3/2 = ±3/2
x - 3/2 = 3/2
x = 3/2 + 3/2
x = 6/2 ÷ 2/2
x = 3
x - 3/2 = -3/2
x = -3/2 + 3/2
x = 0
5. 7x² = 15x
7x² - 15x = 0
7x² ÷ 7 - 15x ÷ 7 = 0 ÷ 7
x² - 15/7x = 0
x² - 15/7x + 225/196 = 0 + 225/196
(x - 15/14)² = 225/196
√(x - 15/14)² = √225/196
x - 15/14 = ± 15/14
x - 15/14 = 15/14
x = 15/14 + 15/14
x = 30/14 ÷ 2/2
x = 15/7
x - 15/14 = -15/14
x = -15/14 + 15/14
x = 0
