Answer:
To complete the square, 36 should be added to both sides.
Step-by-step 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
