Solar quadratic expression by completing the square. x^2+12x+22=0. Choose the appropriate form.

Answer 1

x² + 12x + 22 = 0 [subtract 22 from both sides to get:

x² + 12x = -22 [find a number to add to "x² + 12x" that makes it a perfect square. That number will be the square of half of the number in front of the "x". The number in front of the "x" is 12. Half of 12 is 6 and 6² = 36 so we add 36 to both sides of the equation to get:

x² + 12x + 36 = -22 + 36

x² + 12x + 36 = 14 [write the left side as a "square". The number grouped with "x" will be 6:

(x + 6)² = 14 [take the square root of both sides:

x + 6 = ±√14 [subtract 6 from both sides:

x = -6 ± √14

So the answers are x = -6 + √14 and x = -6 - √14