https://file.aiquickdraw.com/mathbot/file/1726688583575hxw3ok1f.jpg

The equation in the image is:

\[
x^2 - 8x + 11 = 0
\]

To solve this equation by completing the square, follow these steps:

1. Start with the equation:

\[
x^2 - 8x + 11 = 0
\]

2. Move the constant (11) to the other side:

\[
x^2 - 8x = -11
\]

3. To complete the square, take half of the coefficient of \(x\), which is \(-8\). Half of \(-8\) is \(-4\), and then square it:

\[
(-4)^2 = 16
\]

4. Add 16 to both sides of the equation to maintain equality:

\[
x^2 - 8x + 16 = -11 + 16
\]

\[
x^2 - 8x + 16 = 5
\]

5. Now, the left side is a perfect square trinomial:

\[
(x - 4)^2 = 5
\]

6. Take the square root of both sides:

\[
x - 4 = \pm \sqrt{5}
\]

7. Solve for \(x\):

\[
x = 4 \pm \sqrt{5}
\]

So, the solutions are:

\[
x = 4 + \sqrt{5} \quad \text{or} \quad x = 4 - \sqrt{5}
\]

Would you like further details on any step? Here are some related questions for practice:

1. What is the general process for completing the square?
2. How do you solve a quadratic equation using the quadratic formula?
3. Can all quadratic equations be solved by completing the square?
4. How can you recognize a perfect square trinomial?
5. What is the difference between completing the square and factoring?

**Tip:** Completing the square is particularly useful for deriving the quadratic formula and solving quadratic equations that are not easily factorable.

Solve the following equation by completing the square: x^2 - 8x + 11 = 0

Learn how to solve the quadratic equation x^2 - 8x + 11 = 0 using the method of completing the square. This step-by-step guide explains the concept and provides practice for students in Grades 9-11.

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