Find the solution to the following equation by transforming it into a perfect square trinomial:

\[ x^2 - 12x = 13 \]

Options:
A. \{46, 55\}
B. \{-1, 13\}
C. \{-15, 27\}
D. \{-21, 33\}

x 2 − 12 x = 13 ⇔ x 2 − 2 ⋅ x ⋅ 6 + 6 2 − 6 2 = 13 ⇔ ( x − 6 ) 2 = 13 + 36 ⇔ ( x − 6 ) 2 = 49 ⇔ ( x − 6 ) 2 = 7 2 x − 6 = 7 or x − 6 = − 7 x = 13 x = − 1 A n s . x ∈ { − 1 , 13 }

Answered by kate200468 | 2024-06-10

x² -12x = 13 way to obtain 36 > (-12/2)² = 36 x² -12x + 36 =13 +36 since we add 36 to the left,we must also add 36 to the right (x-6)² = 49 x-6 = 7 x = 7 + 6 = 13 or -7 + 6 = -1 x = -1 or 13

Answered by Poknoy | 2024-06-10

The solutions to the equation x 2 − 12 x = 13 are x = 13 and x = − 1 . This is found by completing the square transforming the equation into ( x − 6 ) 2 = 49 . Therefore, the correct answer is option B: { -1, 13 }.
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Answered by kate200468 | 2024-12-20