Solving Quadratic Equations

 $4\sqrt{5}\ +\ 3\sqrt{?}$ 
 In order to add these radicals what number has to take the place of the question mark?

 $\left(\sqrt{6}\right)^2$  

What is the reduced answer?

• 6

• 36

•  $\sqrt{6}$  

What is the reduced and simplified answer for $\sqrt{8}+5\sqrt{2}$  

•  $5\sqrt{10}$  

•  $5\sqrt{16}$  

•  $7\sqrt{2}$  

Complete the simplification of a radical $\sqrt{54}=?\sqrt{6}$   

What number should replace the question mark?

 $x^2\ +\ 5x\ =\ -6$  

What is the first step to solving using the Zero Product Property?

• take the square root

• set the equation equal to zero

• Factor out the x

 $2x^2-\ 18x\ =\ 0$  

The equation is set equal to zero, what is the second step to solve using zero product property?

• Factor out the GCF

• Find 2 numbers that add to 2 and multiply to 18

• Take the square root of both sides

 $2x^2-\ 18x\ =\ 0$ 
What are the factors for this equation? 

• (x - 9)(x + 2) = 0

• x = -2 and x = 18

• 2x(x-9) = 0

 $x^2\ +\ 5x\ =\ -6$  

Set the equation equal to zero.

•  $x^2+5x-6=0$  

•  $x^2+5x+6=0$ 

•  $x^2=-5x\ -6$ 

 $2x\left(x-\ 9\right)=\ 0$ 
What are the two equations you will create to solve using the zero product property? 

• 2x = 0

• x - 9 = 0

• 2x = 0  OR    x - 9 = 0

 $2x^2-\ 18x\ =\ 0$  

What are the solutions to this equation?  (Factor out the GCF.)

• x = 0 and x = 9

• x = $\frac{1}{2}$  

• x = 2   or    x = -2