To solve the quadratic equation \( 2x^2 - 5x = 6 \), we first rearrange it into standard form:
\[ 2x^2 - 5x - 6 = 0 \]
Next, we can use the quadratic formula:
\[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \]
In our case, \( a = 2 \), \( b = -5 \), and \( c = -6 \).
Now we calculate the discriminant (\( b^2 - 4ac \)):
\[ b^2 - 4ac = (-5)^2 - 4 \cdot 2 \cdot (-6) = 25 + 48 = 73 \]
Now plug the values into the quadratic formula:
\[ x = \frac{-(-5) \pm \sqrt{73}}{2 \cdot 2} = \frac{5 \pm \sqrt{73}}{4} \]
Now we approximate \( \sqrt{73} \):
\[ \sqrt{73} \approx 8.544 \]
Now we can calculate the two possible solutions for \( x \):
\[ x_1 = \frac{5 + 8.544}{4} = \frac{13.544}{4} \approx 3.386 \]
\[ x_2 = \frac{5 - 8.544}{4} = \frac{-3.544}{4} \approx -0.886 \]
Rounding these solutions to the nearest hundredth, we have:
- \( x_1 \approx 3.39 \)
- \( x_2 \approx -0.89 \)
Thus, the solutions to the quadratic equation \( 2x^2 - 5x = 6 \) are approximately \( 3.39 \) and \( -0.89 \). Please select the appropriate solution based on the context or further information provided in your question.
1 answer