https://file.aiquickdraw.com/mathbot/file/1728619935742ku1ye8g4.jpg

The equation given in the image is:

\[
(x - 2)^2 + 3 = 9
\]

Let's solve this step by step:

1. Subtract 3 from both sides of the equation to isolate the squared term:

\[
(x - 2)^2 = 9 - 3
\]
\[
(x - 2)^2 = 6
\]

2. Take the square root of both sides to solve for \( x - 2 \):

\[
x - 2 = \pm \sqrt{6}
\]
\[
x - 2 = \pm 2.449
\]

3. Add 2 to both sides to solve for \( x \):

\[
x = 2 \pm 2.449
\]

This gives two possible solutions:

\[
x = 2 + 2.449 = 4.449
\]
\[
x = 2 - 2.449 = -0.449
\]

So the solutions in decimal form are:

\[
x = 4.449 \quad \text{or} \quad x = -0.449
\]

Do you have any questions or want more details on any step?

### Related Questions:
1. How do you handle equations with different powers of \(x\)?
2. Can you solve a similar equation with \( (x - a)^3 + b = c \)?
3. What is the process for solving inequalities that involve squares?
4. How does squaring affect negative numbers when solving equations?
5. Can all quadratic equations be solved by taking square roots?

### Tip:
When taking the square root of both sides of an equation, remember to include both the positive and negative roots!

Learn how to solve the equation (x - 2)^2 + 3 = 9 with a detailed step-by-step explanation. This problem involves algebraic manipulation, understanding quadratic equations, and applying the square root property. Suitable 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