https://file.aiquickdraw.com/mathbot/file/1729308915686dh36kiq9.jpg

Let's solve the equation \( x^2 - 16x + 62 = 0 \) by completing the square.

### Step 1: Move the constant term to the other side
First, rewrite the equation as:
\[
x^2 - 16x = -62
\]

### Step 2: Complete the square
To complete the square, take half of the coefficient of \(x\) (which is \(-16\)) and square it. Half of \(-16\) is \(-8\), and squaring \(-8\) gives \(64\).

Now, add \(64\) to both sides of the equation:
\[
x^2 - 16x + 64 = -62 + 64
\]
\[
x^2 - 16x + 64 = 2
\]

### Step 3: Write the left-hand side as a perfect square
The left-hand side is now a perfect square trinomial:
\[
(x - 8)^2 = 2
\]

### Step 4: Solve for \(x\)
Take the square root of both sides:
\[
x - 8 = \pm \sqrt{2}
\]

So, the two possible solutions for \(x\) are:
\[
x = 8 \pm \sqrt{2}
\]

Thus, the solutions are:
\[
x = 8 + \sqrt{2} \quad \text{or} \quad x = 8 - \sqrt{2}
\]

Let me know if you'd like further details on any step or if you have questions!

### Questions for Expansion:
1. How does completing the square compare to the quadratic formula?
2. What are some real-world applications of completing the square?
3. Can all quadratic equations be solved using completing the square?
4. How does the discriminant relate to the type of solutions in this problem?
5. How would you solve a quadratic equation if it had complex solutions?

### Tip:
When completing the square, always remember to balance the equation by adding the same value to both sides!

Solve the equation for all values of x by completing the square: x^2 - 16x + 62 = 0.

Learn how to solve the quadratic equation x^2 - 16x + 62 = 0 by completing the square. This step-by-step guide helps you understand key algebraic concepts like 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