2xsquare-6x+3=0 by completing square method

x = 2.36603 or 0.633975

Step-by-step explanation:

Here we want to solve the quadratic equation using the completing the square method.

2x^2-6x + 3 = 0

divide through by 2 first;

x^2 - 3x + 3/2 = 0

x*2 - 3x = - 3/2

Half the x term will be - 3/2 and squaring it is 9/4

we add this to both sides

x^2-3x/2 + 9/4 = - 3/2 + 9/4

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

Finding square root of both sides

x-3/2 = √ (3/4)

x = 3/2 ± √ (3/4)

x = 3/2 + √ (3/4) or x = 3/2-√ (3/4)

which becomes

x = 2.36603 or 0.633975