Solving Quadratics by Completing the Square

Find the value of  $c$   that makes  $x^2+14x+c$   a perfect square.

• 7

• 14

• 156

• 49

Solve  $x^2-8x+10=30$  by completing the square.

•  $\left\{-2,\ 10\right\}$  
  

•  $\left\{2,\ -10\right\}$  
  

•  $\left\{2,\ 10\right\}$  
  

• ∅
  

Solve  $x^2+8x+10=3$  by completing the square.

•  $\left\{-1\right\}$  
  

•  $\left\{-1,\ -7\right\}$  
  

•  $\left\{-1,\ 7\right\}$  
  

• ∅
  

Find the value of  $c$   that makes  $x^2-24x+c$   a perfect square.

• 12

• 24

• 144

• 576

Solve  $x^2-6x-16=0$  by completing the square.

•  $\left\{-2,\ 8\right\}$  
  

•  $\left\{-8,\ 2\right\}$  
  

•  $\left\{2,\ 8\right\}$  
  

• ∅
  

Solve  $3x^2+12x+81=15$  by completing the square.

•  $\left\{-4,\ 8\right\}$  
  

•  $\left\{-8,\ 4\right\}$  
  

•  $\left\{4,\ 8\right\}$  
  

• ∅
  

Solve  $5x^2-10x=25$  by completing the square. Round to the nearest 10th if necessary. 

•  $\left\{1.4,\ 3.4\right\}$  
  

•  $\left\{-3.4,\ -1.4\right\}$  
  

•  $\left\{-1.4,\ 3.4\right\}$  
  

• ∅
  

Suppose the rate of flow of a 60-foot-wide river is given by the equation  $r=-0.01x^2+0.6x$ , where  $r$  is the rate in miles per hour and x is the distance from the shore in feet. John does not want to paddle his canoe against a current that is faster than 5 miles per hour. At what distance from the river bank must he paddle in order to avoid a current of 5 miles per hour?

• 6 feet

• 5 feet

• 1 foot

• 10 feet