To find the solutions to the quadratic equation \(2x^2 - 5x = 6\), we first rearrange the equation into standard form:
\[ 2x^2 - 5x - 6 = 0 \]
Next, we can use the quadratic formula to find the solutions. The quadratic formula is given by:
\[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \]
In our equation, the coefficients are:
- \(a = 2\)
- \(b = -5\)
- \(c = -6\)
Substituting these values into the formula:
- Calculate the discriminant (\(b^2 - 4ac\)):
\[ b^2 - 4ac = (-5)^2 - 4 \cdot 2 \cdot (-6) = 25 + 48 = 73 \]
- Substitute the values into the quadratic formula:
\[ x = \frac{-(-5) \pm \sqrt{73}}{2 \cdot 2} = \frac{5 \pm \sqrt{73}}{4} \]
- Calculate \(x\):
Now we compute \(\sqrt{73}\) which is approximately \(8.544\):
\[ x = \frac{5 \pm 8.544}{4} \]
This gives us two potential solutions:
- For the positive root:
\[ x = \frac{5 + 8.544}{4} = \frac{13.544}{4} \approx 3.386 \]
- For the negative root:
\[ x = \frac{5 - 8.544}{4} = \frac{-3.544}{4} \approx -0.886 \]
Finally, rounding both results to the nearest hundredth:
- The first solution rounded is \(3.39\)
- The second solution rounded is \(-0.89\)
Thus, the solutions to the quadratic equation \(2x^2 - 5x - 6 = 0\), rounded to the nearest hundredth, are \(3.39\) and \(-0.89\).
1 answer