To solve the quadratic equation \(2x^2 - 9x = 4\), we first rearrange it into standard form:
\[ 2x^2 - 9x - 4 = 0 \]
Next, we can use the quadratic formula \(x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\), where \(a = 2\), \(b = -9\), and \(c = -4\).
Calculating the discriminant:
\[ b^2 - 4ac = (-9)^2 - 4(2)(-4) = 81 + 32 = 113 \]
Now substituting back into the quadratic formula:
\[ x = \frac{-(-9) \pm \sqrt{113}}{2 \cdot 2} \] \[ x = \frac{9 \pm \sqrt{113}}{4} \]
Next, we calculate \(\sqrt{113}\) (approximately 10.63014581273465):
So we have two potential solutions:
\[ x = \frac{9 + 10.63014581273465}{4} \approx \frac{19.63014581273465}{4} \approx 4.9075 \]
and
\[ x = \frac{9 - 10.63014581273465}{4} \approx \frac{-1.63014581273465}{4} \approx -0.4075 \]
Rounding these to the nearest hundredth gives:
- \(x \approx 4.91\)
- \(x \approx -0.41\)
Now let's match these results against the provided responses. Rounding "4.91" matches one of the options.
Thus, the correct answer is:
x = 4.91