Math-9-Lesson-drtxtxrxrdrdtcydWelcome to Gboard clipboard, any text you copy will be saved here.Welcome to Gboard clipboard, any text you copy will be savedfdyfyfyf here.3.pdf

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

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

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

Complete the square, and show what the
perfect square is:
x
x 12
2
 36
12
2

 x
x  2
6

x
y
y 14
2
 49
14
2

 y
y  2
7

y
y
y 10
2
 25
10
2

 y
y  2
5

y
x
x 5
2

4
25
5
2

 x
x
2
2
5







x

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 (Monday’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

Ex 1: Solve by Completing the Square
2
6 16 0
x x
  
2
6 16
x x
 
+9 +9
2
6 9 25
x x
  
 
2
3 25
x  
 
3 5
x   
3 5
x   8
x  2
x  

2
2 5 0
x x
  
2
2 5
x x
 
+1 +1
2
2 1 6
x x
  
 
2
1 6
x  
 
1 6
x   
1 6
x  

2
10 4 0
x x
  
2
10 4
x x
 
+25 +25
2
10 25 29
x x
  
 
2
5 29
x  
5 29
x   
5 29
x   

Ex: 4Solve by Completing the Square
0
11
8
2


 x
x
11
8
2


 x
x
+16 +16
5
16
8
2


 x
x
  5
4
2


x
  5
4 


x
5
4 


x

Ex 5:The coefficient of x2 must be
“1”
0
3
3
2 2


 x
x
0
2
3
2
3
2


 x
x
16
33
4
3
2








x
2
3
2
3
2

 x
x
4
3
2
2
3


2 9 9
16 16
3 3
2 2
x x
 
 
16
33
4
3



x
16
33
4
3



x
2 2 2 2
33
4
4
33
3


x

Ex 6: The coefficient of x2 must be
“1”
2
3 12 1 0
x x
  
2 1
4
3
x x
  
2
4 4
1
4
3
x x
  
 
 
2 11
2
3
x  
11
2
3
x   
11
2
3
x   3
3

33
2
3
x  

33
2
3
x  
6
3
6 33
3
x



Math-9-Lesson-drtxtxrxrdrdtcydWelcome to Gboard clipboard, any text you copy will be saved here.Welcome to Gboard clipboard, any text you copy will be savedfdyfyfyf here.3.pdf

More Related Content

Similar to Math-9-Lesson-drtxtxrxrdrdtcydWelcome to Gboard clipboard, any text you copy will be saved here.Welcome to Gboard clipboard, any text you copy will be savedfdyfyfyf here.3.pdf (20)

More from RoseyAckerman (20)

Recently uploaded (20)

Math-9-Lesson-drtxtxrxrdrdtcydWelcome to Gboard clipboard, any text you copy will be saved here.Welcome to Gboard clipboard, any text you copy will be savedfdyfyfyf here.3.pdf