Question

What is the solution set of 2x(x - 1) = 3

Answer 1

Complete the square:

expand:
2x^2 - 2x = 3
divide by 2
x^2 - x = 3/2
add the square of half of the coefficient on x to both sides.
x^2 - x + 1/4 = 3/2 + 1/4
x^2 - x + 1/4 = 7/4
factor:
(x - 1/2)^2 = 7/4
square root:
|x - 1/2| = sqrt(7)/2
x -1/2 = sqrt(7)/2 or x - 1/2 = -sqrt(7)/2
x = sqrt(7)/2 + 1/2 or x = 1/2 - sqrt(7/2)

or:

x = 1/2(1 +/- sqrt(7))

Answer 2

2x*2 -2x -3 =0
2 +/- radical ( 4 + 24) 2+/- radical 28 2+/- 2radical 7
x_1,_2 = ------------------ = ------------- = ------------- =
4 4 4
2(1+/- radical 7) 1+/- radical 7
= -------------- = ------------
4 2