Donnie is solving the equation \(2x^2 = 27 + 3x\) using the quadratic formula.

What values should he use for \(a\), \(b\), and \(c\)?

2 x 2 = 27 + 3 x 2 x 2 − 3 x − 27 = 0 a = 2 , b = − 3 , c = − 27 Δ = b 2 − 4 a c = ( − 3 ) 2 − 4 ∗ 2 ∗ ( − 27 ) = 9 + 216 = 225 x 1 ​ = 2 a − b − Δ ​ ​ = 2 ∗ 2 3 − 225 ​ ​ = 4 3 − 15 ​ = 4 − 12 ​ = − 3 x 2 ​ = 2 a − b + Δ ​ ​ = 2 ∗ 2 3 + 225 ​ ​ = 4 3 + 15 ​ = 4 18 ​ = 2 9 ​ = 4.5

Answered by Lilith | 2024-06-10

To solve the equation 2 x 2 = 27 + 3 x , the values for the quadratic formula are identified as a = 2 , b = − 3 , and c = − 27 . Donnie can then use these coefficients to find the solutions for x using the quadratic formula. The standard form of the equation helps to clearly identify the coefficients needed for the calculation.
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Answered by Lilith | 2024-12-23