Let's solve the quadratic equation \( b^2 + 4b = 5 \) using the method of completing the square.

### Step 1: Start with the equation
\[
b^2 + 4b = 5
\]

### Step 2: Move the constant to the other side
Subtract 5 from both sides to get:
\[
b^2 + 4b - 5 = 0
\]

Or you can isolate the quadratic and linear terms on the left-hand side:
\[
b^2 + 4b = 5
\]

### Step 3: Complete the square
To complete the square, take the coefficient of \(b\), which is 4, divide it by 2, and then square the result:
\[
\left(\frac{4}{2}\right)^2 = 2^2 = 4
\]

Add 4 to both sides of the equation:
\[
b^2 + 4b + 4 = 5 + 4
\]

This simplifies to:
\[
(b + 2)^2 = 9
\]

### Step 4: Solve for \(b\)
Take the square root of both sides:
\[
b + 2 = \pm \sqrt{9}
\]
\[
b + 2 = \pm 3
\]

### Step 5: Solve for \(b\)
Now, solve for \(b\) by isolating it:
\[
b = -2 + 3 = 1 \quad \text{or} \quad b = -2 - 3 = -5
\]

### Final Answer:
The solutions are \( b = 1 \) and \( b = -5 \).

Would you like more details or have any questions?

---

Here are 8 related questions:
1. Why is completing the square useful in solving quadratic equations?
2. How can completing the square be used to derive the quadratic formula?
3. What are the advantages of completing the square over factoring?
4. How do you complete the square for a quadratic equation with a leading coefficient other than 1?
5. What is the geometric interpretation of completing the square?
6. How does completing the square help in graphing a quadratic function?
7. Can completing the square be used to solve any quadratic equation?
8. How can you use completing the square to find the vertex of a parabola?

**Tip:** Completing the square is also a key step in converting a quadratic equation into vertex form, which is useful for graphing.

Learn how to solve the quadratic equation b^2 + 4b = 5 using the method of completing the square. This problem covers key algebraic concepts, including quadratic equations and completing the square. Suitable for high school students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation