The product of three and a squared number is twice the sum of the number and four.

Translate the statement into an equation using a variable \( x \) to represent the number.

\[ 3x^2 = 2(x + 4) \]

From the text of the task we can write the equation:
3 x 2 = 2 ( x + 4 ) 3 x 2 = 2 x + 8 3 x 2 − 2 x − 8 = 0 Δ = ( − 2 ) 2 − 4.3. ( − 8 ) = 4 + 96 = 100 x = 2.3 2 ± 100 ​ ​ = 6 2 ± 10 ​ x 1 ​ = 6 2 − 10 ​ = − 6 8 ​ = − 3 4 ​ x 2 ​ = 2.3 2 + 10 ​ = 6 12 ​ = 2

Answered by Ryan2 | 2024-06-10

3 x 2 = 2 ( x + 4 ) 3 x 2 = 2 x + 8 3 x 2 − 2 x − 8 = 0 3 x 2 − 6 x + 4 x − 8 = 0 3 x ( x − 2 ) + 4 ( x − 2 ) = 0 ( 3 x + 4 ) ( x − 2 ) = 0 x = − 3 4 ​ ∨ x = 2

Answered by konrad509 | 2024-06-10

The equation representing the statement is 3 x 2 = 2 ( x + 4 ) . After rearranging, we get 3 x 2 − 2 x − 8 = 0 which can be solved using the quadratic formula. The positive solution for x is 2.
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Answered by Ryan2 | 2024-10-31