Solving the Absolute Value Quadratic: |x² - 6x + 8| = 0

To solve the equation $|x^2 - 6x + 8| = 0$, recognize that the absolute value of a number is zero if and only if the number itself is zero. Therefore, we set the expression inside the absolute value to zero:

$x^2 - 6x + 8 = 0$

Next, we attempt to factor the quadratic expression:

The expression $x^2 - 6x + 8$ can be factored into:

$(x - 2)(x - 4) = 0$

Now, apply the zero product property, which states if a product equals zero, at least one of the factors must be zero. So, set each factor equal to zero:

• $x - 2 = 0$ gives $x = 2$
• $x - 4 = 0$ gives $x = 4$

Thus, the solutions to the equation $|x^2 - 6x + 8| = 0$ are:

$x = 2$ and $x = 4$.