Solving Perfect Square Equations

3.5 Solving Quadratic Equations by Completing the Square 2

On Tuesday...

We saw that we can use the square root property after factoring one side of the equation if it was a perfect square trinomial.

What happens when one side is not a perfect square?

• We will CREATE one!

• This process is called completing the square

• The first step is to find the term that will make it a perfect square

• Ex:  $x^2+16x=17$  

Once you have you perfect square:

• Solve using the square root property!

• Ex:

   $x^2+16x+64=81$  

Let's Do Another:

• Ex:

   $x^2+10x-11=0$  

One More...

• Ex:

   $x^2+4x-12=0$  

Open Ended

Now you: What number should be added to complete the square?

$$x^2+14x$$  

Open Ended

What number should be added to complete the square?

$$x^2+6x$$  

Open Ended

Solve by completing the square:

$$x^2-10x+24=0$$  

Open Ended

Solve by completing the square:

$$x^2+10x+9=0$$