To solve the equation [tex]\( d^2 = \frac{1}{3} a - f \)[/tex] for [tex]\( a \)[/tex], follow these steps:
1. Start with the given equation:
[tex]\[
d^2 = \frac{1}{3} a - f
\][/tex]
2. Isolate [tex]\( \frac{1}{3} a \)[/tex] on one side of the equation:
[tex]\[
d^2 + f = \frac{1}{3} a
\][/tex]
3. Clear the fraction by multiplying both sides of the equation by 3. This will eliminate the denominator:
[tex]\[
3(d^2 + f) = a
\][/tex]
4. Simplify the expression:
[tex]\[
a = 3d^2 + 3f
\][/tex]
Thus, the solution for [tex]\( a \)[/tex] in terms of [tex]\( d \)[/tex] and [tex]\( f \)[/tex] is:
[tex]\[
a = 3d^2 + 3f
\][/tex]
