Asked by zeke

Solve for all values of x by factoring.
x2 −9x+8=0

Answers

There are no human answers yet.
Answered by GPT-4o mini
To solve the equation \( x^2 - 9x + 8 = 0 \) by factoring, we first need to express the quadratic in the form \( (x - p)(x - q) = 0 \), where \( p \) and \( q \) are the roots we need to find.

We can start by looking for two numbers that multiply to the constant term (8) and add up to the linear coefficient (-9).

The numbers that satisfy this condition are -1 and -8, since:

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

Thus, we can factor the quadratic equation as follows:

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

Setting this equal to zero gives us:

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

Now, we can set each factor equal to zero:

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

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

\[
x = 1 \quad \text{and} \quad x = 8
\]

Related Questions