Sienna is solving the quadratic equation by completing the square.

3*x*2 + 9*x* – 4 = 0

      3*x*2 + 9*x* = 4

   *A*(*x*2 + 3*x*) = 4

What is the value of *A*?

–4

–3

3

4

To solve the quadratic equation by completing the square, Sienna started with the equation:

\[
3x^2 + 9x - 4 = 0
\]

She then moved the constant term to the other side:

\[
3x^2 + 9x = 4
\]

Next, Sienna factored out a common factor from the left side:

\[
3(x^2 + 3x) = 4
\]

Here, \( A \) is the factor that was factored out from the expression \( 3(x^2 + 3x) = 4 \). Since the expression inside the parentheses is \( x^2 + 3x \), the factor \( A \) is the coefficient of \( x^2 \) that was factored out, which is \( 3 \).

**Answer:** The value of \( A \) is \( 3 \).

Would you like more details on completing the square, or do you have any questions? Here are some related questions:

1. How do you complete the square for a quadratic equation?
2. Why is completing the square a useful method for solving quadratics?
3. How do you solve a quadratic equation after completing the square?
4. What are the steps to rewrite a quadratic function in vertex form?
5. Can completing the square be used for any quadratic equation?

**Tip:** When completing the square, remember to balance the equation by adding or subtracting the same value on both sides after forming the perfect square trinomial.

Learn how to solve the quadratic equation 3x^2 + 9x - 4 by completing the square with a detailed step-by-step guide. Understand the process of moving constant terms, factoring, and finding the value of the factor A. 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