Solve the Quadratic Equation: -2x² + 22x - 60 = 0

To solve this quadratic equation, we will use the quadratic formula. Let's go through the process step-by-step:

• Step 1: Identify the coefficients.

The coefficients are $a = -2$, $b = 22$, and $c = -60$.

• Step 2: Calculate the discriminant.

The discriminant $D$ is calculated using the formula $b^2 - 4ac$.
Here, $D = 22^2 - 4(-2)(-60) = 484 - 480 = 4$.

• Step 3: Apply the quadratic formula.

The quadratic formula is $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$.
Substituting the values, we get $x = \frac{-22 \pm \sqrt{4}}{2(-2)}$.

• Step 4: Simplify and solve for $x$.

The expression inside the square root is $\sqrt{4} = 2$.
Therefore, we have two potential solutions:
$x_1 = \frac{-22 + 2}{-4} = \frac{-20}{-4} = 5$
$x_2 = \frac{-22 - 2}{-4} = \frac{-24}{-4} = 6$.

The solutions to the equation $-2x^2 + 22x - 60 = 0$ are $x_1 = 5$ and $x_2 = 6$.

In conclusion, the solution to the problem is:

$x_1=5$ $x_2=6$