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Solving quadratic equation by completing the square. Help me please
1. 5p^2 + 2p -9=0
2. 2y^2 -3y-8=0

Sagot :

Rider21idn
Solving Quadratic Equation by Completing the Square:
ALWAYS REMEMBER the standard form of a Quadratic Equation is Ax2 + Bx + C = 0.   1.       5p2  + 2p – 9 = 0  
First ALWAYS make your A=1. In this case, you need to DIVIDE the whole equation by 5.  

So, we can have:    
(5p2  + 2p – 9)/5 = 0/5    
p2 + 2/5 p – 9/5 = 0    
p2 + 2/5 p = 9/5  

Next get (B/2)2 and ADD it to the terms on the LEFT and RIGHT side of the equation.  
(B/2)2  =   {(2/5)(1/2)}2             
           = (1/5)2  
(B/2)2  = 1/25  

p2 + 2/5 p + 1/25 = 9/5 + 1/25  

This time we have completed the square (the Left side of the equation is a perfect square; it can be factored completely)   And we will have:  

(p + 1/5)2  =  (45+1)/25  
(p + 1/5)2  =  46/25  

Then take the square root of both sides of the equation for us to get the roots. We have:  

p +1/ 5 = √(46/25)
p + 1/5  = (√46)/5  
p = +/-  (√46)/5  - 1/5  

So you now have the roots that will satisfy your equation:  

P1 = (√46)/5  - 1/5                                              p2 = - (√46)/5  - 1/5                        
     P1   = {(√46)-1} / 5       ANSWER                   p2 = - {(√46)-1} / 5  ANSWER
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