Solve the equation by completing the square:

\[ m^2 + 2m - 48 = -6 \]

m 2 + 2 m − 48 = − 6 m 2 + 2 m − 48 + 6 = 0 m 2 + 2 m − 42 = 0 a = 1 , b = 2 , c = − 42 Δ = b 2 − 4 a c = 2 2 − 4 ∗ 1 ∗ ( − 42 ) = 4 + 168 = 172 Δ ​ = 172 ​ = 4 ∗ 43 ​ = 2 43 ​ x 1 ​ = 2 a − b − Δ ​ ​ = 2 − 2 − 2 43 ​ ​ = 2 2 ( − 1 − 43 ​ ) ​ = − 1 − 43 ​ x 2 ​ = 2 a − b + Δ ​ ​ = 2 − 2 + 2 43 ​ ​ = 2 2 ( − 1 + 43 ​ ) ​ = − 1 + 43 ​

Answered by Lilith | 2024-06-10

m 2 + 2 m − 48 = − 6 m 2 + 2 m ⋅ 1 + 1 2 − 1 2 = − 6 + 48 ( m + 1 ) 2 − 1 = 42 ( m + 1 ) 2 = 42 + 1 ( m + 1 ) 2 = 43 ⟺ m + 1 = − 43 ​ ∨ m + 1 = 43 ​ m = − 1 − 43 ​ ∨ m = − 1 + 43 ​

Answered by Anonymous | 2024-06-10

To solve the equation by completing the square, we rewrite the equation, complete the square, and find that the solutions are m = − 1 + 43 ​ and m = − 1 − 43 ​ .
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Answered by Lilith | 2024-10-24