Solve x2 + 2x – 48 = –6 by completing the square.
Question 13 options:

A) 



B) 



C) 



D) 



To solve the quadratic equation \( x^2 + 2x - 48 = -6 \) by completing the square, follow these steps:

### Step 1: Move the constant term to the other side
First, move the constant term \( -48 \) to the right side by adding 48 to both sides:

\[
x^2 + 2x = -6 + 48
\]

\[
x^2 + 2x = 42
\]

### Step 2: Complete the square
Next, we complete the square on the left-hand side. To do this, take half of the coefficient of \( x \), which is 2, divide it by 2, and then square it:

\[
\left( \frac{2}{2} \right)^2 = 1
\]

Add this value to both sides of the equation:

\[
x^2 + 2x + 1 = 42 + 1
\]

\[
(x + 1)^2 = 43
\]

### Step 3: Solve for \( x \)
Now, take the square root of both sides:

\[
x + 1 = \pm \sqrt{43}
\]

\[
x = -1 \pm \sqrt{43}
\]

Thus, the solutions are:

\[
x = -1 + \sqrt{43} \quad \text{or} \quad x = -1 - \sqrt{43}
\]

Therefore, the answer in simplified form is:

\[
x = -1 \pm \sqrt{43}
\]

### Want more details?
Feel free to ask if you'd like further clarification or have any additional questions!

### Related questions:
1. What are the advantages of solving quadratics by completing the square?
2. How does completing the square compare to using the quadratic formula?
3. Can every quadratic equation be solved by completing the square?
4. How would the solution change if the quadratic had a different constant term?
5. What are the real-life applications of solving quadratic equations?

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

Solve x^2 + 2x – 48 = –6 by completing the square.

Learn how to solve the quadratic equation x^2 + 2x - 48 = -6 by completing the square with a detailed step-by-step solution. This method highlights key algebraic techniques for students in Grades 9-11.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation