How to complete the square???

Question

I just got into this today, I'm having a hard time understanding my teacher. Will anyone help me??

Here's and example that's NOT one of my questions. I want to know HOW not the answer:

3x² + 5x - 1

Answer 1

3x² + 5x - 1 = 0

Rewrite the equation as 3x² + 5x = 1

Divide both sides by 3 (so that the coefficient of x² is 1): x² + (5/3)x = 1/3

Find half of the coefficient of x and square that number: [(1/2)(5/3)]² = 25/36

Add 25/36 to both sides: x² + (5/3)x + (25/36) = 1/3 + 25/36 = 37/36

Factor the left side as a perfect square and solve for x:

(x + 5/6)² = 37/36

x + 5/6 = ±√37 / 6

x = [-5 ± √37] / 6