2 4 Completing the Square Objective To complete

2. 4 Completing the Square • Objective: To complete a square for a quadratic equation and solve by completing the square

Main step in order 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 +2 ab + b² • 3. ) We take ½ of the X coefficient or b (Divide the number in front of the X by 2) • 4. ) Then square that number

To Complete the Square x 2 + 6 x • Take ½ the coefficient of ‘x’ or b/2 3 • Square it and add it 9 x 2 + 6 x + 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 (tommorrow’s lesson)

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