Problem with completing the square - 4x^2 + 3x - 2 = 0?

Question

I've tried using the qudratic form, the answers given are same as what I got. But using the completing the square method of ( x + b/2) ^2 the answers differs from the quadratic formula answer. is this suppose to happen?

Answer 1

Question Number 1 :

For this equation 4*x^2 + 3*x - 2 = 0 , answer the following questions :

A. Use completing the square to find the root of the equation !

Answer Number 1 :

The equation 4*x^2 + 3*x - 2 = 0 is already in a*x^2+b*x+c=0 form.

By matching the constant position, we can derive that the value of a = 4, b = 3, c = -2.

1A. Use completing the square to find the root of the equation !

  4*x^2 + 3*x - 2 = 0 ,divide both side with 4

  By doing so we get x^2 + 0.75*x - 0.5 = 0 ,

  We know that the coefficient of x is 0.75

  We have to use the fact that ( x + q )^2 = x^2 + 2*q*x + q^2 , and assume that q = 0.75/2 = 0.375

  Next, we have to separate the constant to form x^2 + 0.75*x + 0.140625 - 0.640625 = 0

  Which is the same with ( x + 0.375 )^2  - 0.640625 = 0

  Which can be turned into (( x + 0.375 ) - 0.800390529679106 ) * (( x + 0.375 ) + 0.800390529679106 ) = 0

  And it is the same with ( x + 0.375 - 0.800390529679106 ) * ( x + 0.375 + 0.800390529679106 ) = 0

  So we just need to add up, and get ( x - 0.425390529679106 ) * ( x + 1.17539052967911 ) = 0

  We get following answers x1 = 0.425390529679106 and x2 = -1.17539052967911

Answer 2

The answer is the same if you use the quadratic formula or completing the square.

-4x²+3x-2=0

quadratic formula

x=(-3±√(3²-4*-4*-2))/(2*-4)

=(-3±√(-23))/-8

=(3±√(-23))/8

So there are no real solutions but two complex/imaginary solutions.

-4x²+3x-2=0

completing the square

-4x²+3x=2

x²-(3/4)x=2/-4

x²-(3/4)x+(9/64)=(-1/2)+(9/64)

(x-(3/8))²=-23/64

x-(3/8)=±√(-23/64)

x=±√(-23/64)+(3/8)

x=(±√(-23)/8)+(3/8)

x=(3±√(-23))/8

Same answer.