Solve the Quadratic Equation: x²-6x+8=0 for Parameter x

To solve this quadratic equation by factoring, follow these steps:

• Step 1: Write the equation: $x^2 - 6x + 8 = 0$.
• Step 2: Find two numbers that multiply to $+8$ (the constant term) and add up to $-6$ (the coefficient of $x$).

These numbers are $-2$ and $-4$, since $(-2) \times (-4) = 8$ and $(-2) + (-4) = -6$.

• Step 3: Rewrite the quadratic expression as $(x - 2)(x - 4) = 0$.
• Step 4: Solve each factor separately:
  • $x - 2 = 0 \Rightarrow x = 2$
  • $x - 4 = 0 \Rightarrow x = 4$

Therefore, the solutions to the quadratic equation $x^2 - 6x + 8 = 0$ are $x = 2$ and $x = 4$.

The correct choice for the solution is:

$x=2,x=4$ which corresponds to choice 4.