Solve the following equation for a,a. Be sure to take into account whether a letter is capitalized or not.
d, squared, equals, one third, a, minus, f
d 
2
 =
3
1
​
 a−f

The given equation is:

\[
d^2 = \frac{1}{3}a - f
\]

We are tasked with solving for \( a \).

### Steps to solve for \( a \):

1. Start with the equation:
   \[
   d^2 = \frac{1}{3}a - f
   \]

2. Add \( f \) to both sides to isolate the term with \( a \) on the right-hand side:
   \[
   d^2 + f = \frac{1}{3}a
   \]

3. Multiply both sides by 3 to eliminate the fraction:
   \[
   3(d^2 + f) = a
   \]

4. Simplify the right-hand side:
   \[
   a = 3(d^2 + f)
   \]

Thus, the solution for \( a \) is:
\[
a = 3(d^2 + f)
\]

Let me know if you would like further details or explanations on any step!

---

### Related Questions:
1. How do you solve linear equations involving fractions?
2. How would the equation change if \( f \) were a function of \( d \)?
3. What if the equation was \( d^2 = \frac{a}{3} - f \), instead?
4. How does factoring play a role in solving quadratic equations?
5. What are some common errors when solving equations with fractions?

### Tip:
When solving equations with fractions, it's often helpful to multiply through by the denominator to simplify the equation early on.

Solve the following equation for a. Be sure to take into account whether a letter is capitalized or not: d^2 = (1/3)a - f.

Learn how to solve the equation d^2 = (1/3)a - f for variable a using algebraic methods. This problem involves isolating variables and eliminating fractions, suitable for students in Grades 8-10.

Math Problem Statement

Solve the following equation for a,a. Be sure to take into account whether a letter is capitalized or not. d, squared, equals, one third, a, minus, f d 2

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation