To solve the equation \((x - 8)^2 = 81\), follow these steps:

1. Take the square root of both sides to remove the square:
   \[
   x - 8 = \pm \sqrt{81}
   \]
   Since the square root of 81 is 9:
   \[
   x - 8 = \pm 9
   \]

2. Now, solve for \(x\) by considering both the positive and negative values of 9:
   
   For the positive root:
   \[
   x - 8 = 9
   \]
   Add 8 to both sides:
   \[
   x = 17
   \]

   For the negative root:
   \[
   x - 8 = -9
   \]
   Add 8 to both sides:
   \[
   x = -1
   \]

Thus, the solutions are \(x = 17\) and \(x = -1\).

Would you like further explanation on any step?

---

Here are 5 related questions for further practice:

1. Solve \((x + 5)^2 = 49\).
2. Solve \((2x - 3)^2 = 16\).
3. Solve \((x - 4)^2 = 64\).
4. Solve \( (x - 6)^2 = 36\).
5. Solve \( (x + 7)^2 = 121 \).

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

Discover how to solve the equation (x - 8)² = 81 step-by-step by using the square root method. This algebra problem involves key concepts such as solving quadratic equations and applying the square root property. Ideal for students in Grades 7-9.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation