Solve the quadratic equation using the quadratic formula:

\[ 2x^2 + 9x - 4 = 0 \]

2 x 2 + 9 x − 4 = 0 / : 2 x 2 + 2 9 ​ x − 2 = 0 x 2 + 2 x ⋅ 4 9 ​ + ( 4 9 ​ ) 2 − ( 4 9 ​ ) 2 = 2 ( x + 4 9 ​ ) 2 − 16 81 ​ = 2 ( x + 4 9 ​ ) 2 = 16 32 ​ + 16 81 ​ ( x + 4 9 ​ ) 2 = 16 113 ​ ⟺ x + 4 9 ​ = − 16 113 ​ ​ ∨ x + 4 9 ​ = 16 113 ​ ​ x = − 4 9 ​ − 4 113 ​ ​ ∨ x = − 4 9 ​ + 4 113 ​ ​ x = − 4 9 + 113 ​ ​ ∨ x = − 4 9 − 113 ​ ​

Answered by Anonymous | 2024-06-10

2 x 2 + 9 x − 4 = 0 a = 2 , b = 9 , c = − 4 Δ = b 2 − 4 a c = 9 2 − 4 ∗ 2 ∗ ( − 4 ) = 81 + 32 = 113 x 1 ​ = 2 a − b − Δ ​ ​ = 4 − 9 − 113 ​ ​ x 2 ​ = 2 a − b + Δ ​ ​ = 4 − 9 + 113 ​ ​

Answered by Lilith | 2024-06-10

To solve the equation 2 x 2 + 9 x − 4 = 0 , we apply the quadratic formula after identifying the coefficients. The solutions are x 1 ​ = 4 − 9 + 113 ​ ​ and x 2 ​ = 4 − 9 − 113 ​ ​ . These represent the values of x that satisfy the quadratic equation.
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Answered by Anonymous | 2024-10-15