Solve by completing the square.

-x² + 6x + 13 = 0

Be careful, because a = -1, not a = 1 like we need. First divide everything by -1.

x² – 6x – 13 = 0

Ah, much better. Now we can see  is 3, so add/subtract 3² = 9.

(x² – 6x + 9) – 13 – 9 = 0

Factor the stuff on the left, and move everything else to the right.

(x – 3)² = 22

 and 

Square completed.

Solve by completing the square.

2x² – x – 4 = 0

Start by clearing out the a term.

Looks like  is - , so square that.

Easy does it on those fractions; they can get gnarly real quickly.

Solve by completing the square.

Having a fraction for a doesn't really change anything. Just multiply through by 2 to clear it out.

x² + 10x + 2 = 0

Now cut b = 10 in half and square it:  is 5, and 5² = 25.

(x² + 10x + 25) + 2 – 25 = 0

(x + 5)² = 25 – 2

 and