https://file.aiquickdraw.com/mathbot/file/1728671277220sbwe9jn5.jpg

Let's solve the quadratic equation \(x^2 - 8x + 16 = 0\) by completing the square.

### Step 1: Write the equation in the form \(x^2 - 8x = -16\).

We already have:
\[
x^2 - 8x + 16 = 0
\]
Subtract 16 from both sides:
\[
x^2 - 8x = -16
\]

### Step 2: Complete the square.

To complete the square, take half of the coefficient of \(x\), which is \(-8\), divide by 2, and square it. 

\[
\left(\frac{-8}{2}\right)^2 = 16
\]

Add 16 to both sides to complete the square:

\[
x^2 - 8x + 16 = 0
\]

Now the left side is a perfect square trinomial:

\[
(x - 4)^2 = 0
\]

### Step 3: Solve for \(x\).

Take the square root of both sides:

\[
x - 4 = 0
\]

Solve for \(x\):

\[
x = 4
\]

Thus, the solution is:
\[
x = 4
\]

Would you like more details on any step or have any questions?

### Related Questions:
1. How do you complete the square for a general quadratic equation?
2. What if the quadratic equation had a different constant term, like \(x^2 - 8x + 12 = 0\)?
3. Can you apply completing the square for equations where the coefficient of \(x^2\) is not 1?
4. How does completing the square relate to the quadratic formula?
5. What are other methods for solving quadratic equations?

### Tip:
When completing the square, always ensure the coefficient of \(x^2\) is 1. If it's not, divide the whole equation by the coefficient before proceeding!

Solve the equation by completing the square. x^2 - 8x + 16 = 0

Learn how to solve the quadratic equation x^2 - 8x + 16 = 0 using the method of completing the square. This detailed step-by-step solution covers algebraic concepts of completing the square and solving quadratic equations. 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