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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 = ± ( subtract 6 from both sides )

k = - 6 ± , thus

k = - 6 - ≈ - 12.56 or k = - 6 + ≈ 0.56