To solve the quadratic equation \(2x^2 - 5x = 6\), we first rearrange it into standard form:
\[ 2x^2 - 5x - 6 = 0 \]
Next, we can either complete the square or use the quadratic formula. Here, we'll use the quadratic formula:
\[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \]
In our equation, \(a = 2\), \(b = -5\), and \(c = -6\).
Now, we calculate the discriminant \(b^2 - 4ac\):
\[ b^2 - 4ac = (-5)^2 - 4(2)(-6) = 25 + 48 = 73 \]
Now plug in the values into the quadratic formula:
\[ x = \frac{-(-5) \pm \sqrt{73}}{2(2)} \]
This simplifies to:
\[ x = \frac{5 \pm \sqrt{73}}{4} \]
Now we need to calculate both potential solutions:
Calculating \( \sqrt{73} \): \[ \sqrt{73} \approx 8.544 \]
Finding the two solutions:
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First solution: \[ x_1 = \frac{5 + 8.544}{4} = \frac{13.544}{4} \approx 3.386 \]
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Second solution: \[ x_2 = \frac{5 - 8.544}{4} = \frac{-3.544}{4} \approx -0.886 \]
Rounding to the nearest hundredth:
- \(x_1 \approx 3.39\)
- \(x_2 \approx -0.89\)
Thus, among the choices provided:
- x = -0.89 is a solution.
Therefore, the correct response is:
x = -0.89.