Solving Quadratic Equations by Completing the Square

Solve the quadratic Equation by completing the square.  Round off to 1 decimal place. 

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

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

Solve the quadratic Equation by completing the square round off to 2 decimal places.

Answer explanation

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

Answer explanation

 $x^2-12x+9=0$   $x^2-12x+\left(\frac{-12}{2}\right)^2-\left(\frac{-12}{2}\right)^2+9=0$  
 $x^2-12x+36-36+9=0$  
 $\left(x-6\right)^2-27=0$ 
 $\sqrt{\left(x-6\right)^2}=\sqrt{27}$  
 $x-6=\pm5.20$  
 $x=5.20+6=11.20$  
 $x=-5.20+6=0.80$   

Solve the quadratic Equation by completing the square.  Round off to 2 decimal places

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

  $14+x-3x^2=4$    $3x^2-x-14+4=0$  
 $\frac{3x^2}{3}-\frac{x}{3}-\frac{10}{3}=0$ 
 $x^2-\frac{1}{3}x+\left(\frac{1}{6}\right)^2-\left(\frac{1}{6}\right)^2-\frac{10}{3}=0$ 
 $\left(x-\frac{1}{6}\right)^2-\frac{1}{36}-\left(\frac{10}{3}\times\frac{12}{12}\right)$  

 $\left(x-\frac{1}{6}\right)^2-\frac{1}{36}-\frac{120}{36}=0$  

 $\left(x-\frac{1}{6}\right)^2-\frac{121}{36}=0$   $\sqrt{\left(x-\frac{1}{6}\right)^2}=\sqrt{\frac{121}{36}}$    $x-\frac{1}{6}=\pm\frac{11}{6}$   $x=\pm\frac{11}{6}+\frac{1}{6}$   $x=2,\frac{-5}{3}$  

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

 $x^2-6x+\left(\frac{-6}{2}\right)^2-\left(\frac{-6}{2}\right)^2+1$   $x^2-6x+9-9+1$ 
  $\left(x-3\right)^2-8$  

Answer explanation

 $x^2+3x+\left(\frac{3}{2}\right)^2-\left(\frac{3}{2}\right)^2-2$   $x^2+3x+\frac{9}{4}-\frac{9}{4}-2$ 
  $\left(x+\frac{3}{2}\right)^2-\frac{17}{4}$  

Answer explanation

 $x^2+12x+\left(\frac{12}{2}\right)^2-\left(\frac{12}{2}\right)^2$   $x^2+12x+36-36$ 
  $\left(x+6\right)^2-36$