To solve the quadratic equation \(2x^2 - 5x = 6\), we first rearrange it to standard form:
\[ 2x^2 - 5x - 6 = 0 \]
Next, we can use the quadratic formula \(x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\), where \(a = 2\), \(b = -5\), and \(c = -6\).
- Calculate the discriminant:
\[ b^2 - 4ac = (-5)^2 - 4(2)(-6) = 25 + 48 = 73 \]
- Substitute into the quadratic formula:
\[ x = \frac{-(-5) \pm \sqrt{73}}{2(2)} = \frac{5 \pm \sqrt{73}}{4} \]
- Now, calculate the two possible solutions:
\[ x_1 = \frac{5 + \sqrt{73}}{4} \] \[ x_2 = \frac{5 - \sqrt{73}}{4} \]
Calculating these:
- For \(x_1\):
\[ \sqrt{73} \approx 8.544 \] \[ x_1 \approx \frac{5 + 8.544}{4} \approx \frac{13.544}{4} \approx 3.386 \]
- For \(x_2\):
\[ x_2 \approx \frac{5 - 8.544}{4} \approx \frac{-3.544}{4} \approx -0.886 \]
Rounding \(x_2\) to the nearest hundredth gives \(x_2 \approx -0.89\).
Thus, the solution to the quadratic equation \(2x^2 - 5x = 6\) rounded to the nearest hundredth is:
x = -0.89.
So, the correct response is:
x equals -0.89.