To find the solutions to the quadratic equation \( 2x^2 - 5x = 6 \), we first rearrange the equation into standard form:
\[ 2x^2 - 5x - 6 = 0 \]
Next, we can solve this quadratic equation using the quadratic formula:
\[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \]
Here, \( a = 2 \), \( b = -5 \), and \( c = -6 \).
Calculating the discriminant:
\[ b^2 - 4ac = (-5)^2 - 4 \cdot 2 \cdot (-6) = 25 + 48 = 73 \]
Now, substituting into the quadratic formula:
\[ x = \frac{-(-5) \pm \sqrt{73}}{2 \cdot 2} = \frac{5 \pm \sqrt{73}}{4} \]
Now we calculate \( \sqrt{73} \), approximately \( 8.544 \):
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Calculating the two possible values of \( x \):
For the positive root:
\[ x = \frac{5 + 8.544}{4} = \frac{13.544}{4} \approx 3.386 \]
For the negative root:
\[ x = \frac{5 - 8.544}{4} = \frac{-3.544}{4} \approx -0.886 \]
Next, rounding \( -0.886 \) to the nearest hundredth gives \( -0.89 \).
Thus, the solution to the equation rounded to the nearest hundredth is:
\[ \boxed{-0.89} \]
From the options provided, \( x = -0.89 \) is the correct response.