Answer:
k = - 12.56 or k = 0.56
Step-by-step explanation:
Given
k² + 12k = 7
To complete the square
add ( half the coefficient of the k- term )² to both sides
k² + 2(6)k + 36 = 7 + 36, that is
(k + 6)² = 43 ( take the square root of both sides )
k + 6 = ± [tex]\sqrt{43}[/tex] ( subtract 6 from both sides )
k = - 6 ± [tex]\sqrt{43}[/tex], thus
k = - 6 - [tex]\sqrt{43}[/tex] ≈ - 12.56 or k = - 6 + [tex]\sqrt{43}[/tex] ≈ 0.56
