14.4B completing the square

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

14.4B completing the square

You need your notebook and Ipad

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

$$x^2+bx+c=0$$

$$x^2+bx+c=0$$

$${(x+\frac{b}{2})}^2+c-{(\frac{b}{2})}^2=0$$

Note 14.4B: Completing the square

Example: Solve:

First step: 

Solving the equation:

                                                                               or 

                                                                               or

$$x^2+18x+17=0$$

$${(x+\frac{18}{2})}^2+17-{(\frac{18}{2})}^2=0$$

$${(x+9)}^2+17-9^2=0$$

$${(x+9)}^2+17-81=0$$

$${(x+9)}^2-64=0$$

$${(x+9)}^2=64$$

$$x+9=8$$

$$x+9=-8$$

$$x=-1$$

$$x=-17$$

Solve by completing the square

$$x^2+12x-13=0$$

Bettermarks

• Work on 14.4B
• Raise your finger if you have any questions or when you're finished