3.3 Notes Part 2_Alg2

3.3 Notes Part 2

Solve using Sq Rts - PSTs

Make a PST

Solve by Completing the Square

Perfect Square Trinomial

• a² + 2ab + b² = (a + b)(a + b) = (a + b)²

• a² - 2ab + b² = (a - b)(a - b) = (a - b)²

• For example: 4x² - 12x + 9 = (2x)² - 2(2x)(3) + (3)²

• = (2x - 3)(2x - 3) = (2x - 3)²

• Check: FOIL (2x - 3)(2x - 3)

• 4x² - 6x - 6x + 9

• 4x² - 12x + 9

Multiple Choice

Solve:

4x² - 12x + 9 = 25

• x = -0.5 or x = -5.5

• x = -8 or x = 8

• x = -1 or x = 4

Solve:  $4x^2-12x+9=25$  

•  $(2x-3)^2=25$  

•  $\sqrt{\left(2x-3\right)^2}=\sqrt{25}$  

•  $2x\ -3\ =\pm5$  

•  $2x-3=5\ \ or\ \ 2x-3=-5$  

•  $2x=8\ \ or\ \ 2x\ =\ -2$  

• x = 4 or x= -1

Complete the square:  $x^2+10x$  

• This is in the form  $x^2+bx$  

• Take b and divide it in 2:  $\frac{b}{2}$  

• square b divided by 2:  $\left(\frac{b}{2}\right)^2$  

•  $\left(\frac{b}{2}\right)^2$  completes the square

•  $\left(\frac{b}{2}\right)^2=\left(\frac{10}{2}\right)^2=\left(5\right)^2=25$  

Multiple Choice

Complete the square.

x² + 14x + _

• x² + 14x - 196

• x² + 14x + 49

• x² + 14x - 49

• x² + 14x + 196

Multiple Choice

Complete the square for

x² - 12x + _

• x² - 12x + 144

• x² - 12x + 36

• x² - 12x - 36

• x² - 12x - 144

Solve by completing the square:  $x^2+14x+2=0$  

• Check to see if you can factor "like normal"

• If you can't, get the equation into the form  $x^2+bx=c$  

•  $x^2+14x=-2$  

• Find the number that will complete the square on the left:  $x^2+14x+\ \ \ =-2+\ \ \$  

Solve by completing the square:  $x^2+14x+2=0$  

• Find  $\left(\frac{b}{2}\right)^2$  

•  $\left(\frac{b}{2}\right)^2=\left(\frac{14}{2}\right)^2=\left(7\right)^2=49$  
  

• Fill in the number that completes the square on BOTH SIDES:  $x^2+14x+49=-2+49$  

• The left side is now a perfect square trinomial. Factor accordingly. Simplify and solve using square roots

Solve by completing the square:  $x^2+14x+2=0$  

•  $x^2+14x+49=47$  
  

•  $\left(x+7\right)^2=47$  
  

•  $\sqrt{\left(x+7\right)^2}=\sqrt{47}$  
  

•  $x+7=\pm\sqrt{47}$  
  

•  $x=-7\pm\sqrt{47}$  

Multiple Choice

Solve by completing the square:

 $x^2-12x\ -3=0$  

•  $x\ =6\pm\sqrt{39}$  

•  $x=\pm12$  

•  $x=-6\pm\sqrt{39}$  

•  $x=6\pm\sqrt{3}$  

•  $x=-6\pm\sqrt{3}$  

Solve by completing the square: $x^2-12x-3=0$  

•  $x^2-12x+\ \ \ \ \ =3+$  

•  $\left(\frac{b}{2}\right)^2=\left(-\frac{12}{2}\right)^2=\left(-6\right)^2=36$  

•  $x^2-12x+36=3+36$  

•  $\left(x-6\right)^2=39$  

•  $\sqrt{\left(x-6\right)^2}=\sqrt{39}$  

•  $x-6=\pm\sqrt{39}\ \ \ \ \ \ Solutions:\ x=6\pm\sqrt{39}$