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 \( c = -6 \).
First, we calculate the discriminant \( b^2 - 4ac \):
\[ b^2 - 4ac = (-5)^2 - 4(2)(-6) = 25 + 48 = 73 \]
Now we can compute the roots:
\[ x = \frac{-(-5) \pm \sqrt{73}}{2(2)} = \frac{5 \pm \sqrt{73}}{4} \]
Calculating the two potential solutions:
- \( x_1 = \frac{5 + \sqrt{73}}{4} \)
- \( x_2 = \frac{5 - \sqrt{73}}{4} \)
Now we approximate \( \sqrt{73} \):
\[ \sqrt{73} \approx 8.544 \]
Calculating \( x_1 \):
\[ x_1 = \frac{5 + 8.544}{4} = \frac{13.544}{4} \approx 3.386 \]
Calculating \( x_2 \):
\[ x_2 = \frac{5 - 8.544}{4} = \frac{-3.544}{4} \approx -0.886 \]
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 negative 0.89.