Solve the equation by factoring.
x squared equals 3 x plus 18
Question content area bottomSolve the equation by factoring.
x squared equals 3 x plus 18
Question content area bottom
Part 1
Rewrite the equation in factored form.
  
enter your response hereequals0 
​(Factor completely.)
Part 2
The solution set is StartSet nothing EndSet
  
.
​(Use a comma to separate answers as needed. Type each solution only​ once.)
Part 1
Rewrite the equation in factored form.
  
enter your response hereequals0 
​(Factor completely.)
Part 2
The solution set is StartSet nothing EndSet
  
.
​(Use a comma to separate answers as needed. Type each solution only​ once.)

To solve the equation by factoring, follow these steps:

### Part 1: Rewrite the Equation in Factored Form

**Step 1: Start with the given equation:**

\[
x^2 = 3x + 18
\]

**Step 2: Move all terms to one side of the equation to set it equal to zero:**

\[
x^2 - 3x - 18 = 0
\]

**Step 3: Factor the quadratic equation:**

To factor \(x^2 - 3x - 18\), we need to find two numbers that multiply to \(-18\) and add to \(-3\). These numbers are \(-6\) and \(3\). 

So, the equation factors as:

\[
(x - 6)(x + 3) = 0
\]

### Part 2: Find the Solution Set

**Step 1: Set each factor equal to zero and solve for \(x\):**

1. \(x - 6 = 0\) ⟹ \(x = 6\)
2. \(x + 3 = 0\) ⟹ \(x = -3\)

**Step 2: Write the solution set:**

\[
\text{Solution set} = \{6, -3\}
\]

So, the factored form of the equation is \((x - 6)(x + 3) = 0\), and the solution set is \(\{6, -3\}\).

---

Would you like a detailed explanation of any of these steps, or do you have any other questions?

Here are 5 related questions to expand on this problem:

1. How do you factor a trinomial where the leading coefficient is not 1?
2. What is the quadratic formula, and how does it compare to factoring for solving quadratic equations?
3. How can you verify the solutions to a factored quadratic equation?
4. What are the possible types of solutions (real or complex) for a quadratic equation?
5. How does completing the square compare to factoring when solving quadratics?

**Tip:** Always check your solutions by substituting them back into the original equation to ensure they satisfy the equation.

Learn how to solve the equation x^2 = 3x + 18 by factoring with a detailed step-by-step solution. This problem covers key algebraic concepts, including factoring quadratic equations and the quadratic equation formula. Suitable for students in Grades 7-9.

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