5.4 Completing the Square Objective: To complete a square for a quadratic equation and solve by completing the square

Review 1 𝑏 2 =25 𝑏 = 25 b = ±5

Review 2 𝑑 2 =12 𝑑 = 12 d = ±2 3 or 3.464

Review 3 𝑑 2 =−18 𝑑 = −18 d = ±3𝑖 2 or 4.242i

Steps to complete the square 1.) You will get an expression that looks like this: AX²+ BX 2.) Our goal is to make a square such that we have (a + b)² = a² +2ab + b² 3.) We take ½ of the X coefficient (Divide the number in front of the X by 2) 4.) Then square that number

To Complete the Square x2 + 6x 3 Take half of the coefficient of ‘x’ Square it and add it 9 x2 + 6x + 9 = (x + 3)2

Complete the square, and show what the perfect square is:

To solve by completing the square If a quadratic equation does not factor we can solve it by two different methods 1.) Completing the Square (today’s lesson) 2.) Quadratic Formula (Next week’s lesson)

Steps to solve by completing the square 1.) If the quadratic does not factor, move the constant to the other side of the equation Ex: x²-4x -7 =0 x²-4x=7 2.) Work with the x²+ x side of the equation and complete the square by taking ½ of the coefficient of x and squaring Ex. x² -4x 4/2= 2²=4 3.) Add the number you got to complete the square to both sides of the equation Ex: x² -4x +4 = 7 +4 4.)Simplify your trinomial square Ex: (x-2)² =11 5.)Take the square root of both sides of the equation Ex: x-2 =±√11 6.) Solve for x Ex: x=2±√11

Solve by Completing the Square +9

Solve by Completing the Square +121

Solve by Completing the Square +1

Solve by Completing the Square +25

Solve by Completing the Square +16

Solve by Completing the Square +9

The coefficient of x2 must be “1”

The coefficient of x2 must be “1”