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

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!

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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.