SOLUTION: Solve by completing the square. 4x^2 = 2x - 3 = 0 I have worked this problem three times now and can not figure it out. Could somebody please help me?????

Question 69251: Solve by completing the square.
4x^2 = 2x - 3 = 0
I have worked this problem three times now and can not figure it out. Could somebody please help me?????
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Solve by completing the square.
Assume that the 1st "=" sign should be +
:
Having 4 as the coefficient of x^2 does complicate matters, however...
4x^2 + 2x - 3 = 0
:
4x^2 + 2x = + 3
:
Make the coefficient of x^2 one, divide equation by 4
x^2 + (2/4)x __ = 3/4
;
x^2 + (1/2)x __ = 3/4
:
Choose a value that completes the square: (1/2)(1/2) =(1/4)^2 = 1/16
x^2 + (1/2)x + (1/16) = (3/4) + (1/16)
:
x^2 + (1/2)x + (1/16) = (12/16) + (1/16)
:
x^2 + (1/2)x + (1/16) = 13/16
:
[x + (1/4)]^2 = 13/16
:
x + (1/4) = +/-Sqrt(13/16)
:
The denominator (16) is a square, extract that (1/4)
x + (1/4) = +/-(1/4)Sqrt(13)
:
x = -(1/4) +/-(1/4)Sqrt(13)
or
x =
and
x =
:
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