Solve Quadratic Equation: -2X² + 6X + 8 = 0

To solve the quadratic equation $-2X^2 + 6X + 8 = 0$ using the quadratic formula, follow these steps:

• Step 1: Calculate the discriminant, $b^2 - 4ac$.

Here, $a = -2$, $b = 6$, and $c = 8$. Plug these into the formula: $b^2 - 4ac = 6^2 - 4(-2)(8) = 36 + 64 = 100$ Since the discriminant is greater than zero, the roots are real and distinct.

• Step 2: Apply the quadratic formula, $X = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$.

Substituting the values, we have: $X = \frac{-6 \pm \sqrt{100}}{2(-2)}$ Simplifying inside the square root gives us: $X = \frac{-6 \pm 10}{-4}$ This leads to two possible solutions: - First, calculate with the positive square root: $X_1 = \frac{-6 + 10}{-4} = \frac{4}{-4} = -1$ - Second, calculate with the negative square root: $X_2 = \frac{-6 - 10}{-4} = \frac{-16}{-4} = 4$

Thus, the solutions to the equation are $X_1 = 4$ and $X_2 = -1$.

Verifying against the choices, the correct choice is: : $X_1=4, X_2=-1$.

Therefore, the solution is $X_1 = 4, X_2 = -1$.