14.4B completing the square

• Wiskunde
• Middelbare school
• vmbo lwoo, havo
• Leerjaar 3

14.4B completing the square

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Solving quadratic equations

x​2​​+13x+36=0

Solving quadratic equations

(x+5)​2​​=0

Solving quadratic equations

(4x−20)​2​​=0

Solving quadratic equations

(x+8)​2​​=100

Solving quadratic equations

(x+8)​2​​=

(x+9)​2​​=

(x+10)​2​​=

Solving quadratic equations

x​2​​+14x+50=

Note 14.4B: Completing the square

You can solve every quadratic equation of the form: 

by completing the square.

First step: Changing                                           to

Second step: solving the equation

x​2​​+bx+c=0

x​2​​+bx+c=0

(x+​2​​b​​)​2​​+c−(​2​​b​​)​2​​=0

Note 14.4B: Completing the square

Example: Solve:

First step: 

Solving the equation:

                                                                               or 

                                                                               or

x​2​​+18x+17=0

(x+​2​​18​​)​2​​+17−(​2​​18​​)​2​​=0

(x+9)​2​​+17−9​2​​=0

(x+9)​2​​+17−81=0

(x+9)​2​​−64=0

(x+9)​2​​=64

x+9=8

x+9=−8

x=−1

x=−17

Solve by completing the square

x​2​​+12x−13=0

Bettermarks

• Work on 14.4B
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