Transform the FF into quadratic equation:

To transform the given equation into a quadratic equation, we start with the equation:

\[
\frac{x + 3}{4} = \frac{6}{x + 3}
\]

First, let's eliminate the fractions by cross-multiplying:

\[
(x + 3)(x + 3) = 4 \times 6
\]

Simplifying both sides:

\[
(x + 3)^2 = 24
\]

Next, expand the left-hand side:

\[
x^2 + 6x + 9 = 24
\]

Now, bring all terms to one side of the equation to set it to zero:

\[
x^2 + 6x + 9 - 24 = 0
\]

Simplify the constant terms:

\[
x^2 + 6x - 15 = 0
\]

This is the quadratic equation formed from the given equation.

Let me know if you need further details or if you have any questions! Here are 5 related questions:

1. Do you want to solve this quadratic equation for \(x\)?
2. Are you interested in the methods used to factor quadratic equations?
3. Would you like to explore the quadratic formula to find the roots of this equation?
4. Do you want to see how to complete the square to solve the quadratic equation?
5. Are you curious about the discriminant and how it helps determine the nature of the roots?

**Tip:** When transforming an equation into a quadratic form, always ensure to simplify the equation fully before solving for the variable \(x\).

Learn how to transform the equation (x + 3)/4 = 6/(x + 3) into a quadratic equation step-by-step. Understand the process of eliminating fractions, expanding terms, and simplifying to form the quadratic equation x^2 + 6x - 15 = 0. Suitable for students in Grades 9-12, covering key algebraic concepts and the quadratic equation formula.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation