What number must you add to complete the square of x2 plus 8x equals 11?

Answer 1

You add 16. Why? Because 16 is the square of half the co-efficient of x.

That's the rule you use, to get the square of x + 4.

Completing the square is useful for solving for x, as the following shows:

x2 + 8x = 11 : given

x2 + 8x + 16 = 27 : add 16 to both sides

x + 4 = ±√27 = ±3√3 : square-root of both sides

x = ±3√3 - 4 : subtract 4 from both sides

(Note, the rule works only when x2 has no express co-efficient.)