Solve this equation by completing the square. 3x2 - 4x = - 2

Solve this equation by completing the square. 3x^2 - 4x = - 2

Step 1:

Divide by the leading coefficient (coef. of x^2), and transpose.

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

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

Complete the square,

(x-2/3) ^2 - 4/9 = - 2/3

Solve for (x-2/3)

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

x-2/3 = ± (√2) i/3

Solve for x

x=2/3± (√2) i/3

or

x = (2± (√2) i) / 3