Solve the quadratic equation by completing the square.

x ≈ - 12.74, x ≈ - 5.26

Step-by-step explanation:

Given

x² + 18x + 67 = 0 ( subtract 67 from both sides )

x² + 18x = - 67

To complete the square

add ( half the coefficient of the x- term )² to both sides

x² + 2(9)x + 81 = - 67 + 81

(x + 9)² = 14 ( take the square root of both sides )

x + 9 = ± ( subtract 9 from both sides )

x = - 9 ±

Hence

x = - 9 - ≈ - 12.74

x = - 9 + ≈ - 5.26

answer: all the values are within because it has a pattern that repeats from -6 to 4.

good luck!