You have the equation:

\[
(x - 3)^2 = 5
\]

To solve for \( x \), follow these steps:

1. Take the square root of both sides to eliminate the square:
   \[
   \sqrt{(x - 3)^2} = \pm \sqrt{5}
   \]
   Which simplifies to:
   \[
   x - 3 = \pm \sqrt{5}
   \]

2. Solve for \( x \) by adding 3 to both sides:
   \[
   x = 3 \pm \sqrt{5}
   \]

Thus, the two solutions for \( x \) are:
\[
x = 3 + \sqrt{5} \quad \text{or} \quad x = 3 - \sqrt{5}
\]

If you want a decimal approximation:
\[
x \approx 3 + 2.236 \quad \text{or} \quad x \approx 3 - 2.236
\]
So:
\[
x \approx 5.236 \quad \text{or} \quad x \approx 0.764
\]

Would you like more details or have any questions about the process?

Here are 5 related questions:
1. What is the method to solve quadratic equations in general?
2. How do you handle negative numbers under square roots?
3. Can complex numbers be a solution to this equation?
4. How can you graph the function \( (x-3)^2 - 5 = 0 \)?
5. What does it mean to "complete the square" in algebra?

**Tip:** Always remember, taking the square root of both sides introduces both the positive and negative roots!

Discover how to solve the equation (x-3)^2=5 by applying the square root property. This step-by-step solution covers important algebraic concepts such as square roots and quadratic equations. Ideal for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation