Question

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Part 1
Solve the following quadratic equation by factoring.
x squared minus x equals 6
Question content area bottom
Part 1
The solution set is StartSet nothing EndSet .
  
​(Simplify your answer. Use a comma to separate answers as​ needed.)

Answer 1

To solve the quadratic equation \( x^2 - x = 6 \) by factoring, we first rearrange the equation to set it to zero:

\[
x^2 - x - 6 = 0
\]

Next, we need to factor the quadratic expression \( x^2 - x - 6 \). We look for two numbers that multiply to \(-6\) (the constant term) and add to \(-1\) (the coefficient of \(x\)).

The numbers that satisfy these conditions are \(-3\) and \(2\) because:

\[
-3 \cdot 2 = -6 \quad \text{and} \quad -3 + 2 = -1
\]

Now we can write the factored form of the equation:

\[
(x - 3)(x + 2) = 0
\]

Setting each factor to zero gives us the possible solutions:

1. \( x - 3 = 0 \) which implies \( x = 3 \)
2. \( x + 2 = 0 \) which implies \( x = -2 \)

Thus, the solution set is:

\[
\{ 3, -2 \}
\]

So, the final answer is:

\(\{ 3, -2 \}\)