H^2+14h=-31 Solve by completing the square
       
      
                
     
    
    
    
    
    2 answers:
            
              
              
                
                
Since the constant has been moved to the left side, you can move on to the next step which is adding (b/2)² to both sides of the equation. 
h² + 14h + (14/2)² = -31 + (14/2)²
Simplify the parenthesis and exponent. 
h² + 14h + 7² = -31 + 7² 
h² + 14h + 49 = -31 + 49 
h² + 14h + 49 = 18 
Factor the expression of the left. 
(h + 7)(h + 7) = 18 
Take the square root of both sides. 
√(h + 7)(h + 7) = ± √9 • 2
(h + 7) = ± 3√2 
h + 7 = ± 3√2 
Subtract 7 from both sides. 
You solutions are: 
h = -7 + 3√2 → -2.7573 → -2.76
h = -7 - 3√2 → -11.2426 → -11.24
                                
             
                    
              
              
                
                
Given   <span>H^2+14h=-31, let's complete the square of the 1st two terms:
h^2 + 14h + (14/2)^2  =  -31 + (14/2)^2
  h^2 + 14h + 49   =   -31 + 49 = 18
   (h+7)^2 = 18
Taking the sqrt of both sides,
h+7 = sqrt (9*2) = 3 sqrt(2)
Solving for h,    h= -7 plus or minus 3 sqrt(2)    (answer)</span>
                                
             
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