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

1
by arve

2014-06-19T09:25:31+08:00
Solving Quadratic Equation by Completing the Square:
ALWAYS REMEMBER the standard form of a Quadratic Equation is Ax2 + Bx + C = 0.   1.       5p+ 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:
(5p+ 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
just do the same for no.2 and you will get the roots of y = square root of 73 over 4 plus 3/4......and the other root is y = negative square root of 73 over 4 plus 3/4..