Chapter 9 Quadratic Equations, Inequalities, and Functions
9.1 The Square Root Property and Completing the Square
Learning Objectives
1. Review the zero-factor property
2. Learn the square root property
3. Solve quadraticc equations of the form ax + b 2 = c by using the square root property
4. Solve quadratic equations by completing the square
5. Solve quadratic equations with solutions that are not real numbers.
Objective 1. Review the zero-factor property
Find all solutions by factoring.
1) x2 + 6x - 27 = 0
2) 6x2 = 6x
3) (2x + 7)(x + 1) = 28x - 2
Objective 2. Learn the square root property
Use the square root property to solve the equation.
4) x2 = 25
5) (x + 20)2 = 64
6) (9t - 7)2 = 6
Objective 3. Solve quadratic equations of the form ax + b 2 = c by using the square root property.
Find the term that should be added to the expression to form a perfect square trinomial. Write the
resulting perfect square trinomial in factored form.
7) x2 + 4x +
8) x2 + 5x +
1
Determine the number that will complete the square to solve the equation after the constant
term has
been written on the right side. Do not actually solve.
9) w2 - 6w - 8 = 0
Objective 4. Solve quadratic equaitons by completing the square.
Solve the equation by completing the square.
10) a 2 - 14a + 24 = 0
11) 7x2 + 2x - 5 = 0
12) 0.1x2 - 0.2x - 0.2 = 0
Objective 5. Solve quadratic equations with solutions that are not real numbers.
Find the nonreal complex solutions of the equation.
13) x2 - 4x + 29 = 0
14) x2 + x + 1 = 0
15) -5x2 - 4x - 4 = 0
2