University:
High School
Course:
High School Algebra
Academic year:

2021
Views:

263

Pages:

5
Author:

heymisslisa84

9.4 Solving Quadratic Equations by Completing the Square Core Concepts Completing the Square Words To complete the square for an expression of the form 1 x² + bx, follow these steps. Step 1 Find one-half of b, the coefficient of x. * x² + 2x * x² + 6x * x² + 9x * (2/2) = 1 * (6/2) = 3 * (9/2) = 4.5 Step 2 Square the result from Step 1. * (1)² = 1 * (3)² = 9 * (4.5)² = 30.25 Step 3 Add the result from Step 2 to x² + bx. * x² + 2x + 1 * x² + 6x + 9 * x² + 9x + 81/4 Factor the resulting expression as the square of a binomial. Algebra x² + bx + (b/2)² = (x + b/2)² *The whole point of this is so we can Factor x² + 2x + 1 x² + 6x + 9 x² + 9x + 81/4 (x + 1)(x + 1) (x + 1)² (x + 3)(x + 3) (x + 3)² (x + 9/2)(x + 9/2) (x + 9/2)² ... now solve using Certainly, here's the breakdown of the image you provided: Textual Content: 9.4 Extra Practice Complete the square for the expression. Then factor the trinomial. x² + 12x (12/2)² = 36 x² + 12x + 36 = (x + 6)² x² - 14x (14/2)² = 49 x² - 14x + 49 = (x - 7)² x² + 4x (4/2)² = 4 x² + 4x + 4 = (x + 2)² x² + 18x (18/2)² = 81 x² + 18x + 81 = (x + 9)² x² - 7x (-7/2)² = 49/4 x² - 7x + 49/4 = (x - 7/2)² x² + 11x (11/2)² = 121/4 x² + 11x + 121/4 = (x + 11/2)² Solve the equation by completing the square. x² - 8x = -15 (8/2)² = 16 x² - 8x + 16 = -15 + 16 (x - 4)² = 1 x - 4 = ±1 x = 5 and x = 3 x² + 2x = 3 (2/2)² = 1 x² + 2x + 1 = 3 + 1 (x + 1)² = 4 x + 1 = ±2 x = 1 and x = -3 x² + 7x = 30 (7/2)² = 49/4 x² + 7x + 49/4 = 30 + 49/4 (x + 7/2)² = 169/4 x + 7/2 = ±13/2 x = 3 and x = -10 x² - 26x = -9 (26/2)² = 169 x² - 26x + 169 = -9 + 169 (x - 13)² = 160 x - 13 = ±√160 x = 13 ± 4√10 x² - 12x = 10 (12/2)² = 36 x² - 12x + 36 = 10 + 36 (x - 6)² = 46 x - 6 = ±√46 x = 6 ± √46 x² - 15x = 18 (15/2)² = 225/4 x² - 15x + 225/4 = 18 + 225/4 (x - 15/2)² = 297/4 x - 15/2 = ±√297/2 x = (15 ± 3√33)/2