Solve the following equation for a,a. Be sure to take into account whether a letter is capitalized or not.
b, squared, equals, start fraction, a, divided by, m, end fraction, minus, H
b 
2
 =
m
a
​
 −H

The equation you provided is:

\[
b^2 = \frac{a}{m} - H
\]

We need to solve for \(a\).

### Step-by-Step Solution:

1. **Start with the given equation:**
   \[
   b^2 = \frac{a}{m} - H
   \]

2. **Isolate the term containing \(a\):**
   To isolate \( \frac{a}{m} \), add \(H\) to both sides:
   \[
   b^2 + H = \frac{a}{m}
   \]

3. **Solve for \(a\):**
   Multiply both sides of the equation by \(m\) to isolate \(a\):
   \[
   a = m(b^2 + H)
   \]

### Final Answer:
\[
a = m(b^2 + H)
\]

Would you like more details or have any questions?

Here are five related questions:
1. What is the solution if \(m = 2\), \(b = 3\), and \(H = 1\)?
2. How do we solve for \(m\) in this equation instead of \(a\)?
3. What if \(H\) equals 0? How does that affect the solution?
4. Can you derive the equation for \(b\) in terms of \(a\), \(m\), and \(H\)?
5. How does the equation change if the term \(b^2\) is replaced by \(b^3\)?

**Tip:** Always check the units of each term in an equation to ensure consistency when solving for variables.

Solve the following equation for a, a. Be sure to take into account whether a letter is capitalized or not.
b^2 = (a/m) - H

Discover how to solve the equation b^2 = (a/m) - H for variable a with step-by-step guidance. This solution highlights key algebraic principles such as isolating variables and equation manipulation. Suitable for high school students in Grades 9-12.

Math Problem Statement

Solve the following equation for a,a. Be sure to take into account whether a letter is capitalized or not. b, squared, equals, start fraction, a, divided by, m, end fraction, minus, H b 2

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