Question

Solve for all values of xx by factoring.
x, squared, minus, 9, x, plus, 8, equals, 0
x
2
−9x+8=
0

Answer 1

To solve the equation \( x^2 - 9x + 8 = 0 \) by factoring, we need to factor the quadratic expression on the left side of the equation.

Step 1: Look for two numbers that multiply to give the constant term (8) and add up to give the coefficient of the linear term (-9).

The two numbers that meet these criteria are -8 and -1, because:

\[
-8 \times -1 = 8
\]
\[
-8 + (-1) = -9
\]

Step 2: Now we can factor the quadratic:

\[
x^2 - 9x + 8 = (x - 8)(x - 1)
\]

Step 3: Set the factored equation equal to zero:

\[
(x - 8)(x - 1) = 0
\]

Step 4: Solve for \( x \) by setting each factor equal to zero:

1. \( x - 8 = 0 \) gives \( x = 8 \)
2. \( x - 1 = 0 \) gives \( x = 1 \)

Thus, the solutions to the equation \( x^2 - 9x + 8 = 0 \) are:

\[
\boxed{8} \quad \text{and} \quad \boxed{1}
\]