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:
\[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \]
In this case, \(a = 2\), \(b = -5\), and \(c = -6\).
Let's calculate the discriminant (\(b^2 - 4ac\)):
\[ b^2 - 4ac = (-5)^2 - 4(2)(-6) = 25 + 48 = 73 \]
Now we can substitute \(a\), \(b\), and the discriminant into the quadratic formula:
\[ x = \frac{-(-5) \pm \sqrt{73}}{2(2)} = \frac{5 \pm \sqrt{73}}{4} \]
Calculating the two possible values for \(x\):
- For \(x_1 = \frac{5 + \sqrt{73}}{4}\)
- For \(x_2 = \frac{5 - \sqrt{73}}{4}\)
Calculating these values:
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Approximately, \[ \sqrt{73} \approx 8.544 \] Thus, \[ x_1 = \frac{5 + 8.544}{4} \approx \frac{13.544}{4} \approx 3.386 \]
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Then, \[ x_2 = \frac{5 - 8.544}{4} \approx \frac{-3.544}{4} \approx -0.886 \]
When rounded to the nearest hundredth, \(x_2 \approx -0.89\).
Thus, the solution to the equation rounded to the nearest hundredth is:
\(x \approx -0.89\)
So the correct answer is:
x = -0.89