Completing the Square (Full process)

Completing the Square (Full process)

The video that is on the next slide is from slide 60 in our Student Notebooks. If you would like to fill it in today, you can or you can copy these steps on separate paper.

• The extra example can be written in example #2's box also

Lesson Video:

https://annotate.net/user/Jessica-Betts/clips/Completing-the-Square-preview

Example 2:

 $x^2+6x-7=0$  

Let's go through the steps together.  You can try them on your own first, if you'd like...if not, we'll walk through them on the next slides.

 $x^2+6x-7=0$  

• Is a=1?

• Move the constant to the other side leave a gap

• Find the missing value:  $\left(\frac{b}{2}\right)^2$  

• Add it to both sides of the equation

• Factor the new trinomial

• Square root both sides and finish solving

Multiple Choice

Step 1: Is our a=1?

• yes, so we are finished with this step

• No, we have to divide the whole equation by that number.

Multiple Choice

Step 2: Move the constant to the other side of the equation. What does the result look like:

• $x^2+6x\ +\ \ \ \ \ \ =7$

• $x^2+6x\ \ \ \ =-7$

• $x^2+6x\ -7\ =\ 7$

• $x^2\ \ \ \ \ \ =-6x+7$

Multiple Choice

Step 3: We find the value that would complete the perfect square binomial

 $\left(\frac{b}{2}\right)^2$  

• +9

• -9

• +36

• 6

Multiple Choice

Step 4: Add that value to both sides of the equation. What would that look like?

• $x^2+6x+9=16$

• $x^2+6x+9=7$

• $x^2+6x\ +9\ =\ -2$

• $x^2+6x-9=-2$

Fill in the Blank

Step 5: Factor the perfect square trinomial. Type in the factors as the binomial squared. Use CMD and the . key to type an exponent or use Shift and 6

Multiple Choice

Step 6: Part a: Take the square root of both sides. What does that look like:

• $x+3=\pm4$

• $x+3=4$

• $x+3=\pm16$

• $x+3=16$

Multiple Select

Step 6 part b: Split that equation into two equations, one for the positve number and one for the negative and solve them both. Select your answers below.

• x=1

• x= -7

• x = -1

• x = 7