Solve the equation:

\[
-149 = x^2 - 24x
\]

− 149 = x 2 − 24 x x 2 − 24 x + 149 = 0 a = 1 b = − 24 c = 149 Δ = ( − 24 ) 2 − 149 ∗ 4 = 576 − 596 → − 20 ​ x 1 ​ ; x 2 ​ = 2 − ( − 24 ) + / − 1 20 ​ ​ = 2 24 + / − 2 i 5 ​ ​ x 1 ​ = 2 24 + 2 i 5 ​ ​ = 2 2 ( 12 + i 5 ​ ) ​ → 12 + i 5 ​ ​ ​ x 2 ​ = 2 24 − 2 i 5 ​ ​ = 2 2 ( 12 − i 5 ​ ​ → 12 − i 5 ​ ​ ​

Answered by mariamikayla | 2024-06-10

− 149 = x 2 − 24 x x 2 − 24 x + 149 = 0 x 2 − 24 x + 144 + 5 = 0 ( x − 12 ) 2 = − 5 x − 12 = − − 5 ​ ∨ x − 12 = − 5 ​ x = 12 − 5 ​ i ∨ x = 12 + 5 ​ i

Answered by konrad509 | 2024-06-10

The equation − 149 = x 2 − 24 x was rearranged to standard quadratic form which is x 2 − 24 x + 149 = 0 . The discriminant was calculated to be -20, indicating two complex solutions: x 1 ​ = 12 + i 5 ​ and x 2 ​ = 12 − i 5 ​ . Therefore, there are no real solutions for the equation.
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Answered by mariamikayla | 2024-12-26