Solving by completing the squares: 4xsquared-8x+3=0?

Answer 1

divide both sides by 4
x^2-2x+3/4=0
(x^2-2x+1)-1+3/4=0
(x-1)^2-1/4=0
(x-1)^2=1/4
x-1=+-1/2
x=3/2,1/2

Answer 2

4x^2 - 8x +3 = 0 , Divide by 4
x^2 - 2x + 3/4 = 0
x^2 - 2x + 1 = -3/4 + 1 = 1/4
(x -1)^2 = 1/4
x-1 = +-1/2
x = 1 + 1/2 = 3/2
x = 1 - 1/2 = 1/2

Answer 3

4x^2-8x+3=0
firstly, get rid of the 3
4x^2-8x=-3
then you get the co-efficient of x^2 = 1 (divide by 4)
x^2-2x=-3/4
then you take the co-efficient of x, halve it, square it, and add it to both sides -> 2,1,1
x^2-2x+1=-3/4+1
x^2-2x+1=1/4
because you just got here by completing the square, you know that this is now a perfect square so now you just solve:
(x-1)^2=1/4
(square root both sides)
x-1=+/-1/2
(add 1 to both sides)
x=1+/-1/2
therefore x=1/2 OR x=1 1/2

Answer 4

4x^2 - 8x +3 = 0
-3 -3
4x^2 - 8x = -3
4(x^2 - 2x) = -3
(x^2 - 2x) = (-3)/4
(x^2 - 2x +1) = (-3)/4 +1
(x-1)^2 = 1/4
x-1 = 1/2 or -1/2
x = (1/2 + 1) or ( -1/2 +1)
x = 3/2 or 1/2

Answer 5

4x^2 - 8x + 3 = 0

4x^2 - 8x = - 3

x^2 - 2x = - 3/4

x^2 - 2x = - 3/4 ----> -2(1/2) = -1 ----> (-1)^2 = 1

x^2 - 2x +1 = - 3/4 + 1

x^2 - 2x +1 = 1/4

(x-1)(x-1) = 1/4

(x-1)^2 = 1/4 ----> take square root of each side.

x-1 = ± 1/2

x = ± 1/2 + 1

x = 1 1/2, - 1/2

Answer 6

4x^2 - 8x = -3
x^2 - 2x = -3/4
x^2 - 2x + 1 = 1 - 3/4 = 1/4
(x-1)^2 = 1/4
x-1 = +/- 1/2
x = 1 1/2 or 1/2

(2x-1)(2x-3) = 0

Answer 7

1st
factor: (2x-3)(2x-1)=0
2nd
.2x-3=0
=>x= 3/2
.2x-1=0
=>x= 2
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