To solve the quadratic equation \(2x^2 - 9x = 4\), we first rearrange the equation into standard form:
\[ 2x^2 - 9x - 4 = 0 \]
Next, we can either factor the equation (if possible), complete the square, or use the quadratic formula:
\[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \]
In this case, \(a = 2\), \(b = -9\), and \(c = -4\).
Let's calculate the discriminant:
\[ b^2 - 4ac = (-9)^2 - 4 \cdot 2 \cdot (-4) = 81 + 32 = 113 \]
Now we will plug these values into the quadratic formula:
\[ x = \frac{-(-9) \pm \sqrt{113}}{2 \cdot 2} = \frac{9 \pm \sqrt{113}}{4} \]
Calculating \( \sqrt{113} \):
\(\sqrt{113} \approx 10.630\)
Now plug this value back into the formula:
\[ x = \frac{9 \pm 10.630}{4} \]
Calculating the two solutions:
- \(x = \frac{9 + 10.630}{4} = \frac{19.630}{4} \approx 4.9075 \approx 4.91\)
- \(x = \frac{9 - 10.630}{4} = \frac{-1.630}{4} \approx -0.4075 \approx -0.41\) (not listed in your options)
Since only one choice rounds to the nearest hundredth, the solution to the quadratic equation \(2x^2 - 9x = 4\) is:
x = 4.91.