https://file.aiquickdraw.com/mathbot/file/1726581804413qqgearo8.jpg

The equation in the image is:

\[
(5 - 3)^2 = 25 - 30 + 9y^2
\]

Let me solve it step by step:

### Step 1: Simplify the left-hand side
\[
(5 - 3)^2 = 2^2 = 4
\]

Thus, the equation becomes:
\[
4 = 25 - 30 + 9y^2
\]

### Step 2: Simplify the right-hand side
\[
25 - 30 = -5
\]

So the equation now is:
\[
4 = -5 + 9y^2
\]

### Step 3: Move \(-5\) to the left-hand side
\[
4 + 5 = 9y^2
\]
\[
9 = 9y^2
\]

### Step 4: Solve for \(y^2\)
\[
y^2 = \frac{9}{9} = 1
\]

### Step 5: Solve for \(y\)
\[
y = \pm 1
\]

Thus, \(y = 1\) or \(y = -1\).

Would you like further details or clarifications? Here are some related questions for further exploration:

1. What are the steps to solve similar quadratic equations?
2. How do you handle equations involving higher powers of variables?
3. Could the equation have had no real solutions, and why?
4. How does this type of equation appear in real-world contexts?
5. How would the solution change if the coefficient of \(y^2\) were different?

**Tip**: Always simplify both sides of an equation step by step to avoid mistakes, especially when dealing with squared terms.

Learn how to solve the quadratic equation (5 - 3)^2 = 25 - 30 + 9y^2 with a detailed step-by-step solution. This problem covers key algebraic concepts, including simplifying expressions and solving quadratic equations. Suitable for students in Grades 7-9.

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