3.3 Notes Part 1_Alg2

3.3 Notes Part 1

Perfect Square Trinomials

Completing the Square

Multiple Choice

Solve for x:

(x + 6)² = 49

• x=7,12

• x=±7

• x=1,-13

• x=43,-55

Solution

 $\left(x+6\right)^2=49$  
 $\sqrt{\left(x+6\right)^2}=\sqrt{49}$  
 $x+6\ =\ \pm7$  
 $x+6=7\ \ or\ \ x+6=-7$  
 $x=1\ \ or\ \ x=-13$  

(x + 6)² = 49 can be written as:

(x + 6)(x + 6) = 49

use F.O.I.L to get

x² + 12x + 36 = 49

The right side of the equation is a perfect square trinomial

because x² + 12x + 36 can be written as a factor squared, (x + 6)²

If asked to solve x² + 12x + 36 = 49, factor and solve using square roots

Recognize PSTs with this formula

Multiple Choice

Is this a perfect square trinomial?
x² + 16x + 64

• Yes
• No

Multiple Choice

Factor: x² + 16x + 64

• (x + 4)²

• (x + 8)²

• (x + 16)²

Multiple Choice

Solve x² + 16x + 64 = 25 using square roots

• x = -3, -13

• x = -3, 3

• x = -13, 13

• x = 5, 8

Solution

 $x^2+16x+64\ =\ 25$  

 $\left(x+8\right)^2=25$  
 $\sqrt{\left(x+8\right)^2}=\sqrt{25}$  
 $x+8\ =\ \pm5$  
 $x+8=5\ \ or\ \ x+8=-5$  
 $x=-3\ \ or\ \ x=-13$  

Multiple Choice

Is this a perfect square trinomial?
x² + 18x + 9

• Yes
• No

Multiple Choice

Is this a perfect square trinomial?

x² - 14x + 49

• Yes

• No

Multiple Choice

Solve:   $x^2-14x+49=-2$  

• x = -9, 5

• x = -7, 7

•  $x=7\pm2i$  

•  $x=7\pm i\sqrt{2}$  

Solve:

 $x^2-14x+49=-2$  

 $\left(x-7\right)^2=-2$  
 $\sqrt{\left(x-7\right)^2}=\sqrt{-2}$  
 $x-7=\pm\sqrt{-2}$  
 $x-7=\pm i\sqrt{2}$  
 $x=7\pm i\sqrt{2}$