Solve the equation by factoring.
x squared equals 5 x plus 14x2=5x+14
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Part 1
Rewrite the equation in factored form.
left parenthesis x minus 7 right parenthesis left parenthesis x plus 2 right parenthesis(x−7)(x+2)equals=0
​(Factor completely.)
Part 2
The solution set is StartSet nothing EndSetenter your response here.

Let's solve the equation by factoring step by step.

### Part 1: Rewrite the equation in factored form

The given equation is:
\[
x^2 = 5x + 14
\]

First, let's move all terms to one side of the equation to set it equal to zero:
\[
x^2 - 5x - 14 = 0
\]

Next, we need to factor this quadratic equation. We are looking for two numbers that multiply to \(-14\) (the constant term) and add to \(-5\) (the coefficient of the \(x\) term). These numbers are \(-7\) and \(2\), so we can factor the quadratic as:
\[
(x - 7)(x + 2) = 0
\]

### Part 2: The solution set

To find the solution set, we set each factor equal to zero:
\[
x - 7 = 0 \quad \text{or} \quad x + 2 = 0
\]

Solving these equations gives:
\[
x = 7 \quad \text{or} \quad x = -2
\]

Therefore, the solution set is:
\[
\{7, -2\}
\]

Would you like more details on how this factoring process works, or do you have any other questions?

Here are 5 related questions to expand your understanding:

1. How would you factor a quadratic equation if the coefficient of \(x^2\) is not 1?
2. Can you explain how the quadratic formula relates to factoring?
3. What happens if a quadratic equation cannot be factored using integers?
4. How do you determine if a quadratic equation has real or complex solutions?
5. What are some methods to check if your factored form is correct?

**Tip:** When factoring quadratics, always double-check by expanding your factors to ensure they match the original equation.

Learn how to solve the quadratic equation x^2 = 5x + 14 by factoring with a detailed step-by-step solution. This problem covers key algebraic concepts, including the quadratic equation and factoring quadratic equations. Suitable for students in Grades 7-9.

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