Solve the equation 4z^2 + 4z -9 = 0 by completeing the square

z=(sqrt(10)-1)/2 or z= -(sqrt(10)-1)//2

Step-by-step explanation:

To complete the square, the last term has to be 1. So adding 10 to both sides, we get:

4z^2+4z+1 = 10

Since 4z^2+4z+1=(2z+1)^2,

(2z+1)^2 = 10.

Taking the square root of both sides, we get

2z+1=sqrt(10) or 2z+1=-sqrt(10)

So z=(sqrt(10)-1)/2 or z= -(sqrt(10)-1)//2

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