To find the solution to the quadratic equation \( 2x^2 - 5x = 6 \), we first rewrite the equation in standard form:
\[ 2x^2 - 5x - 6 = 0 \]
Next, we can use the quadratic formula, which is:
\[ x = \frac{{-b \pm \sqrt{{b^2 - 4ac}}}}{2a} \]
In our equation, \( a = 2 \), \( b = -5 \), and \( c = -6 \).
First, we calculate the discriminant:
\[ b^2 - 4ac = (-5)^2 - 4(2)(-6) = 25 + 48 = 73 \]
Now, we can plug the values into the quadratic formula:
\[ x = \frac{{-(-5) \pm \sqrt{73}}}{2(2)} = \frac{{5 \pm \sqrt{73}}}{4} \]
Next, we calculate \( \sqrt{73} \):
\[ \sqrt{73} \approx 8.544 \]
Now substituting back into the formula:
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For the positive solution: \[ x_1 = \frac{{5 + 8.544}}{4} = \frac{{13.544}}{4} \approx 3.386 \]
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For the negative solution: \[ x_2 = \frac{{5 - 8.544}}{4} = \frac{{-3.544}}{4} \approx -0.886 \]
Rounding \( -0.886 \) to the nearest hundredth gives \( -0.89 \).
Thus, the correct answer is:
x = -0.89