University:
Felician University
Course:
MATH-002 | Basic Math Skills-Algebra
Academic year:

2023
Views:

48

Pages:

2
Author:

CometConductor

**Solve by Completing the Square** Solve each equation by Completing the Square 1) x² - 10x - 56 = 0 x² - 10x + 25 = 56 + 25 (x - 5)² = 81 x - 5 = ±9 x = 5 ± 9 x = 14, -4 2) b² + 2b - 1 = 7 b² + 2b + 1 = 7 + 1 (b + 1)² = 8 b + 1 = ±√8 b = -1 ± √8 b = -1 ± 2√2 3) n² - 32 = 4n n² - 4n - 32 = 0 n² - 4n + 4 = 32 + 4 (n - 2)² = 36 n - 2 = ±6 n = 2 ± 6 n = 8, -4 4) b² + 17b - 69 = -3b + 9 b² + 20b + 100 = 69 + 100 (b + 10)² = 169 b + 10 = ±13 b = -10 ± 13 b = 3, -23 5) 5x² + 20x + 15 = 0 x² + 4x + 3 = 0 x² + 4x + 4 = 3 + 4 (x + 2)² = 7 x + 2 = ±√7 x = -2 ± √7 6) 3m² + m - 24 = 0 m² + (1/3)m - 8 = 0 m² + (1/3)m + 1/36 = 8 + 1/36 (m + 1/6)² = 289/36 m + 1/6 = ±17/6 m = -1/6 ± 17/6 m = 8/3, -3 **Solve each equation by Factoring** 7) x² - 5x - 84 = 0 (x - 12)(x + 7) = 0 x = 12, -7 8) r² - 9r + 8 = 0 (r - 8)(r - 1) = 0 r = 8, 1 9) x² - 3x - 1 = 0 x² - 3x + 9/4 = 1 + 9/4 (x - 3/2)² = 13/4 x - 3/2 = ±√13/2 x = 3/2 ± √13/2 10) n² - 12n + 32 = 0 (n - 6)² = 4 n - 6 = ±2 n = 6 ± 2 n = 8, 4 11) x² + 3x + 4 = 2 x² + 3x + 2 = 0 (x + 2)(x + 1) = 0 x = -2, -1 12) -3n² - 28n = -7n² 4n² - 28n = 0 4(n² - 7n) = 0 n² - 7n = 0 n(n - 7) = 0 n = 0, 7 13) -m² - 7m - 280 = -6m² - 2m 5m² - 5m - 280 = 0 m² - m - 56 = 0 (m - 8)(m + 7) = 0 m = 8, -7 14) 4b² - 24b - 8b + 40 = 0 4b(b - 6) - 5(b - 6) = 0 (4b - 5)(b - 6) = 0 b = 5/4, 6 **Solve each equation by Taking Square Roots** 15) r² = 36 r = ±√36 r = ±6 16) b² = 4 b = ±√4 b = ±2 17) 8x² = 28 x² = 7/2 x = ±√(7/2) 18) -7n² = -252 n² = 36 n = ±√36 n = ±6