To find the solution to the quadratic equation \(2x^2 - 5x = 6\), we first rearrange it into standard form:
\[ 2x^2 - 5x - 6 = 0 \]
Next, we can apply the quadratic formula, which is given by:
\[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \]
In our equation, \(a = 2\), \(b = -5\), and \(c = -6\). Now, we will calculate the discriminant (\(b^2 - 4ac\)):
\[ b^2 - 4ac = (-5)^2 - 4(2)(-6) = 25 + 48 = 73 \]
Now substitute the values into the quadratic formula:
\[ x = \frac{-(-5) \pm \sqrt{73}}{2(2)} = \frac{5 \pm \sqrt{73}}{4} \]
Now, calculating \(\sqrt{73} \approx 8.54\):
So:
\[ x \approx \frac{5 \pm 8.54}{4} \]
Calculating the two solutions:
- \(x_1 = \frac{5 + 8.54}{4} \approx \frac{13.54}{4} \approx 3.385\)
- \(x_2 = \frac{5 - 8.54}{4} \approx \frac{-3.54}{4} \approx -0.885\)
Rounding \(x_1\) and \(x_2\) to the nearest hundredth gives us:
- \(x_1 \approx 3.39\)
- \(x_2 \approx -0.89\)
From the options provided, the correct solution is:
x = -0.89