How do you solve the equation 2x^2-3x+1=0 by completing the square?

1 Answer
George C.
Jan 8, 2017

x=1" " or " "x=1/2

Explanation:

f(x) = 2x^2-3x+1

The difference of squares identity can be written:

a^2-b^2 = (a-b)(a+b)

We will use this with a=(4x-3) and b=1.

First pre-multiply by 8 to avoid the need to do arithmetic with fractions:

0 = 8f(x)

color(white)(0) = 8(2x^2-3x+1)

color(white)(0) = 16x^2-24x+8

color(white)(0) = (4x)^2-2(4x)(3)+9-1

color(white)(0) = (4x-3)^2-1^2

color(white)(0) = ((4x-3)-1)((4x-3)+1)

color(white)(0) = (4x-4)(4x-2)

color(white)(0) = (4(x-1))(2(2x-1))

color(white)(0) = 8(x-1)(2x-1)

So x=1 or x=1/2

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