Solve the following equation by transforming it into a perfect square trinomial:

\[ 3x^2 + 12x = 63 \]

3 x 2 + 12 x = 63 3 x 2 + 12 x − 63 = 0 3 ( x 2 + 4 x − 21 ) = 0 3 [ x 2 + 4 x + 3 x − 3 x − 21 ] = 0 3 [ x 2 + 7 x − 3 x − 21 ] = 0 3 [ x ( x + 7 ) − 3 ( x + 7 )] = 0
3 ( x + 7 ) ( x − 3 ) = 0 x + 7 = 0 or x − 3 = 0 x = − 7 or x = 3

Answered by Lilith | 2024-06-10

To solve the equation 3 x 2 + 12 x = 63 , we first rearranged it and factored out the coefficient of x 2 . By completing the square, we identified the solutions as x = 3 and x = − 7 .
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Answered by Lilith | 2024-12-24