https://file.aiquickdraw.com/mathbot/file/17277902437215oe05nff.jpg

The given quadratic equation is:

\[
(x - 7)^2 = 11
\]

### Step 1: Solve the equation algebraically.

To solve this, first take the square root of both sides:

\[
\sqrt{(x - 7)^2} = \pm \sqrt{11}
\]

This simplifies to:

\[
x - 7 = \pm \sqrt{11}
\]

Now, solve for \( x \):

\[
x = 7 \pm \sqrt{11}
\]

### Step 2: Find the two solutions.

1. **First solution (positive root):**

\[
x = 7 + \sqrt{11} \approx 7 + 3.317 = 10.317
\]

2. **Second solution (negative root):**

\[
x = 7 - \sqrt{11} \approx 7 - 3.317 = 3.683
\]

### Final Answer:

- The smaller of the two solutions is \( x \approx 3.683 \).
- The larger of the two solutions is \( x \approx 10.317 \).

Do you want further details or have any questions?

### Relative Questions:
1. How does taking the square root of both sides help solve a quadratic equation?
2. What are other methods for solving quadratic equations, such as factoring or the quadratic formula?
3. Why do we add and subtract the square root when solving the equation?
4. What is the significance of the plus-minus (\( \pm \)) symbol in solving square root equations?
5. How do you calculate decimal approximations for square roots without a calculator?

### Tip:
When solving quadratic equations, remember to check for both the positive and negative roots when taking square roots of both sides.

For the quadratic equation (x - 7)^2 = 11, complete the table by testing each of the given values to determine whether it is a solution. Identify the two solutions to the quadratic equation.

Learn how to solve the quadratic equation (x - 7)^2 = 11. This step-by-step guide walks through finding the two solutions using algebraic methods, including taking the square root of both sides and applying the plus-minus rule. 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