Solve the quadratic equation by factoring: x^2 - 7x + 10 = 0.

A. x = 2, 5

B. x = -2, -5

C. x = 3, 4

D. x = -3, -4

To solve the quadratic equation \(x^2 - 7x + 10 = 0\) by factoring, follow these steps:

### Step 1: Factor the quadratic expression
We need two numbers that multiply to give \(10\) (the constant term) and add to give \(-7\) (the coefficient of \(x\)).

These two numbers are \(-5\) and \(-2\) because:
\[
-5 \times -2 = 10
\]
\[
-5 + -2 = -7
\]

### Step 2: Write the factored form
Using these two numbers, we can factor the quadratic equation as:
\[
(x - 5)(x - 2) = 0
\]

### Step 3: Solve for \(x\)
Set each factor equal to 0 and solve for \(x\):
\[
x - 5 = 0 \quad \Rightarrow \quad x = 5
\]
\[
x - 2 = 0 \quad \Rightarrow \quad x = 2
\]

### Solution:
The solutions are \(x = 2\) and \(x = 5\). So the correct answer is:

**A. \(x = 2, 5\)**

Would you like more details or have any questions?

### Related questions:
1. How do you solve quadratic equations using the quadratic formula?
2. Can all quadratic equations be factored?
3. What is the difference between factoring and completing the square?
4. How does the discriminant determine the number of solutions for a quadratic equation?
5. What are the applications of solving quadratic equations in real life?

### Tip:
Always check your factored terms by expanding them to ensure the original equation is restored.

Solve the quadratic equation by factoring: x^2 - 7x + 10 = 0.

Learn how to solve the quadratic equation x^2 - 7x + 10 by factoring. This problem demonstrates key algebraic concepts such as factoring quadratic equations and applying the zero product property. Suitable for students in Grades 8-10.

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