University:
Montgomery College
Course:
MATH 130: Elements of Mathematics I: Mathematical Reasoning and Number Systems
Academic year:

2023
Views:

210

Pages:

1
Author:

Camilla House

Mini-Lecture 9.2 Solving Quadratic Equations by Completing the Square Learning Objectives: 1. Write perfect square trinomials. 2. Solve quadratic equations of the form x 2 + bx + c = 0 by completing the square. 3. Solve quadratic equations of the form ax 2 + bx + c = 0 by completing the square. Examples: 1. Solve each quadratic equation by completing the square. a) x 2 + 12 x = −35 b) a 2 − 10a + 21 = 0 c) z 2 + 10 z + 3 = 0 d) x 2 = 7 − 4 x e) x 2 = 5 − 5 x f) a ( 3a − 2 ) + 1 = 5 2. Solve each quadratic equation by completing the square. a) 16 x 2 + 24 x + 5 = 0 b) 9 y 2 + 18 y + 8 = 0 c) 9 x 2 − 35 = 6 x d) 2 x 2 + 4 x + 11 = 0 e) 2n 2 + 6n + 3 = 0 f) 2 x (2 x + 5) = −3 Mixed Practice. Solve each quadratic equation by completing the square. g) k 2 + 8k + 7 = 0 h) x ( 6 x + 1) − 10 = −8 i) 2 x 2 + 5 x − 2 = 0 Teaching Notes: • • • • • Refer students to the textbook for steps used to solve by completing the square: To Solve a Quadratic Equation in x by Completing the Square. Many students will need a review of perfect square trinomials to understand the goal of completing the square. Most students need to see many examples done out for them to understand the process. Some students need to write out both solutions instead of using the “+” symbol. Each section in the text has 3 worksheets in the Extra Practice featuring differentiated learning. −5 ± 3 5 1 ± 13 ; 1f) ; 2 3 −3 ± 3 −5 ± 13 2f) ; 2g) -7, -1; 2a) -1/4, -5/4; 2b) -2/3, -4/3; 2c) 7/3, -5/3; 2d) not real; 2e) 2 4 −5 ± 41 2h) ½, -2/3; 2i) 4 Answers: 1a) -7, -5; 1b) 3, 7; 1c) −5 ± 22 ; 1d) −2 ± 11 ; 1e)