Quadratic Equation Completing the Square

Solve by completing the square. 
 x² − 10x - 11= 0

Solve the following quadratics equation by completing the square... x² + 4x + 1 = 0

• x = -2 ± √3

• x = -3 ± √2

• x = 2 ± √3

• x = 2 ± √2

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

Which of the following trinomials is a perfect square trinomial ?

When factoring
x² - 4x + 4 = 20,
what goes in the blank?
(x - _ )² = 20

Answer explanation

 $\left(x+1\right)^2=9$  
 $\sqrt{\left(x+1\right)^2}=\sqrt{9}$  
 $x+1=\pm3$  
 $x=3-1=2$ 
 $x=-3-1=-4$  

Answer explanation

 $\left(2x+1\right)^2=16$  
 $\sqrt{\left(2x+1\right)^2}=\sqrt{16}$  
 $2x+1=\pm4$  
 $x=\frac{4-1}{2}=\frac{3}{2}$ 
 $x=\frac{-4-1}{2}=\frac{-5}{2}$  

Answer explanation

 $x=\frac{-9-7}{-3}=\frac{16}{3}$   $\left(7-3x\right)^2=81$  
 $\sqrt{\left(7-3x\right)^2}=\sqrt{81}$  
 $7-3x=\pm9$  
 $x=\frac{-9-7}{-3}=\frac{16}{3}$ 
 $x=\frac{9-7}{-3}=\frac{-2}{3}$  

Answer explanation

 $x=-\sqrt{6}-1=-3.45$   $x^2+2x+\left(\frac{2}{2}\right)^2-\left(\frac{2}{2}\right)^2-5=0$  
 $x^2+2x+1-1-5=0$  
 $\left(x+1\right)^2-6=0$ 
 $\sqrt{\left(x+1\right)^2}=\sqrt{6}$  
 $x+1=\pm\sqrt{6}$  
 $x=\pm\sqrt{6}-1$  
 $x=\sqrt{6}-1=1.45$   $x=-\sqrt{6}-1=-3.45$