Question

What number should be added to both sides of the equation to complete the square?

x2 + 12x = 11
36
121
6
144

Answer 1

To complete the square, 36 should be added to both sides.

Explanation:

If you have an equation in the form:

ax² + bx + c = ...

Then to complete the square, you want to convert it to this format:

a²x² + abx + (b/2)² = ...

with all instances of x being on the left.

In this case, we're given x² + 12x = 11. Because the first term has no coefficient, completing the square is much simpler. "a" in this case is just 1, which means that "b" is 12 ÷ 1, or just 12. So:

(b / 2)²

= (12 / 2)²

= 6²

= 36

So to actually complete the square, just add 36 to both sides of the equation:

x² + 12x + 36 = 47

(x + 6)² = 47

You can then solve for x quite easily:

(x + 6)² = 47

x + 6 = ±√47

x = -6 ± √47

Answer 2

Explanation:

Take half of the coefficient of x (in other words, take half of 12). This results in 6. Square this result, obtaining 36.

Now x2 + 12x = 11 becomes x^2 + 12x + 36 = 11 + 36, or

x^2 + 12x + 36 = 47, or

(x + 6)^2 = 47