Question

Quadratic Equations by completing the square
1. r2 + 4r = 5
2. s2 + 4s - 21 = 0
3. 2X2 + 28x = 64

Answer 1

Question

1. r² + 4r = 5

2. s² + 4s - 21 = 0

3. 2x² + 28x = 64

Solution

1. r² + 4r = 5

⟼ r + 4r + 2² = 5 + 2²

⟼ r² + 4r + 4 = 5 + 4

⟼ r² + 4r + 4 = 9

⟼ (r + 2)² = 9

⟼ √(r + 2)² =√9

⟼ r + 2 = 3

⟼ r + 2 = -3

⟼ r = 1

⟼ r = -5

2. s² + 4s - 21 = 0

⟼ s² + 4s - 21 -(-21) = -(-21)

⟼ s² + 4s = 21

⟼ s² + 4s + 2² = 21 + 2²

⟼ s² + 4s + 4 = 25

⟼ (5 + 2)² = 25

⟼ √(5 + 2)² = √2

⟼ 5 + 2 = 5

⟼ 5 + 2 = -5

⟼ 5 = 3

⟼ 5 = -7

3. 2x² + 28x = 64

⟼ 2x² + 28x/2 = 64/2

⟼ x² + 28/2 x = 64/2

⟼ x² + 14x = 32

⟼ x² + 14x + 7² = 32 + 7²

⟼ x² + 14x + 49 = 81

⟼ (x + 7)² = 81

⟼ √(x + 7)² = √81

⟼ x + 7 = 9

⟼ x + 7 = -9

⟼ x = 2

⟼ x = -16.