Solving the Quadratic Equation: -2x² + 4x = 0

To solve this quadratic equation, we will use factoring.

Consider the given equation:
$-2x^2 + 4x = 0$

Step 1: Factor out the greatest common factor from the terms.

The common factor of $-2x^2$ and $4x$ is $2x$. Factoring this out gives:
$2x(-x + 2) = 0$

Step 2: Set each factor to zero.

• $2x = 0$
• $-x + 2 = 0$

Step 3: Solve each equation.

• For $2x = 0$:
  Divide both sides by 2, resulting in: $x = 0$.
• For $-x + 2 = 0$:
  Add $x$ to both sides, giving $2 = x$ or $x = 2$.

Therefore, the solutions to the equation are $x_1 = 2$ and $x_2 = 0$.

The correct answer is choice 4: $x_1 = 2, x_2 = 0$.