**Which of the following procedures in solving the equation 5(x – 3)2 – 20 = 0 is INCORRECT?**

**I. Square both sides of the equation.**

**II. Divide both sides of the equation by 5.**

**III. Add 20 to both sides of the equation.**

**IV. Add 3 to both sides of the equation to obtain the roots.**

**Which of the following procedures in solving the equation 5(x – 3)2 – 20 = 0 is INCORRECT?**

**I. Square both sides of the equation.**

**II. Divide both sides of the equation by 5.**

**III. Add 20 to both sides of the equation.**

**IV. Add 3 to both sides of the equation to obtain the roots.**

IV

II

I

III

Let's go through each option step-by-step for the equation \( 5(x - 3)^2 - 20 = 0 \):

1. **I. Square both sides of the equation.**
   - This is **incorrect** because you don't need to square both sides. The expression \( (x - 3)^2 \) is already squared. Squaring again would introduce unnecessary complexity and could lead to extraneous solutions.

2. **II. Divide both sides of the equation by 5.**
   - This is **correct**. Dividing by 5 simplifies the equation to \( (x - 3)^2 - 4 = 0 \).

3. **III. Add 20 to both sides of the equation.**
   - This is **correct**. Adding 20 to both sides gives \( 5(x - 3)^2 = 20 \), which is part of the normal solving process.

4. **IV. Add 3 to both sides of the equation to obtain the roots.**
   - This is **incorrect**. After simplifying to \( (x - 3)^2 = 4 \), the next step is to take the square root of both sides, giving \( x - 3 = \pm 2 \). Only after solving \( x - 3 = \pm 2 \), do you add 3 to both sides.

### Answer: **I. Square both sides of the equation** is incorrect.

Would you like more details, or do you have any questions?

Here are 5 related questions to expand on this:

1. How do you solve a quadratic equation like \( (x - 3)^2 = 4 \)?
2. Why can squaring both sides of an equation introduce extraneous solutions?
3. What are the roots of the equation \( (x - 3)^2 = 4 \)?
4. Why is it important to divide by constants in algebraic equations?
5. Can all quadratic equations be solved by factoring?

**Tip:** Always check if squaring both sides is necessary or if the equation is already in a squared form, to avoid unnecessary steps.

Which of the following procedures in solving the equation 5(x – 3)^2 – 20 = 0 is INCORRECT? I. Square both sides of the equation. II. Divide both sides of the equation by 5. III. Add 20 to both sides of the equation. IV. Add 3 to both sides of the equation to obtain the roots.

Explore the correct and incorrect procedures in solving the quadratic equation 5(x – 3)^2 – 20 = 0. This problem helps students learn essential algebraic techniques, including dividing by constants and the square root method. Suitable for students in Grades 8-10.

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