Answer:
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 = ± [tex]\sqrt{14}[/tex] ( subtract 9 from both sides )
x = - 9 ± [tex]\sqrt{14}[/tex]
Hence
x = - 9 - [tex]\sqrt{14}[/tex] ≈ - 12.74
x = - 9 + [tex]\sqrt{14}[/tex] ≈ - 5.26
