by using the completing square method find the roots of the equation 4x square +4x+3
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4x^2 + 4x +3 =0
=> x^2 + x + 3/4 =0
=> x^2 + x = -3/4
add (1/2)^2 both side
=> x^2 + x + (1/2)^2 = (1/2)^2 +(-3/4)
=> x^2 +2.x. (1/2) + (1/2)^2 = (-1/2)
=>(x + 1/2)^2 = (-1/2 )
take square root both side
(x + 1/2 )= +_i/root2
x= -1/2 +_i/root2
={-1+_i. root2} /2
=> x^2 + x + 3/4 =0
=> x^2 + x = -3/4
add (1/2)^2 both side
=> x^2 + x + (1/2)^2 = (1/2)^2 +(-3/4)
=> x^2 +2.x. (1/2) + (1/2)^2 = (-1/2)
=>(x + 1/2)^2 = (-1/2 )
take square root both side
(x + 1/2 )= +_i/root2
x= -1/2 +_i/root2
={-1+_i. root2} /2
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