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

\[ x^2 - 10x = 39 \]

x 2 − 10 x = 39 x 2 − 2 ⋅ x ⋅ 5 = 39 / + 5 2 ( ∗ ) x 2 − 2 ⋅ x ⋅ 5 + 5 2 ​ ​ = 39 + 5 2 ( x − 5 ) 2 = 39 + 25 ( x − 5 ) 2 = 64 ⟺ x − 5 = ± 64 ​ x − 5 = − 8 or x − 5 = 8 x = − 8 + 5 or x = 8 + 5 x = − 3 or x = 13

Answered by Anonymous | 2024-06-10

The solutions to the equation x 2 − 10 x = 39 are x = 13 and x = − 3 . This was achieved by transforming the equation into a perfect square trinomial. Completing the square allows for easy solving of quadratic equations.
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Answered by Anonymous | 2024-12-24