We can solve the equation \((2x + 5)^2 = 4\) step by step.

### Step 1: Take the square root of both sides.
\[
\sqrt{(2x + 5)^2} = \pm \sqrt{4}
\]
This simplifies to:
\[
2x + 5 = \pm 2
\]

### Step 2: Solve for \(x\).
Now, we will consider both cases:

1. \(2x + 5 = 2\)
   \[
   2x = 2 - 5
   \]
   \[
   2x = -3
   \]
   \[
   x = -\frac{3}{2}
   \]

2. \(2x + 5 = -2\)
   \[
   2x = -2 - 5
   \]
   \[
   2x = -7
   \]
   \[
   x = -\frac{7}{2}
   \]

### Final Solution:
The two possible solutions are:
\[
x = -\frac{3}{2} \quad \text{or} \quad x = -\frac{7}{2}
\]

Would you like any further details or explanations?

Here are five related questions:
1. How can we solve equations with exponents and radicals?
2. What happens when the square of an expression equals zero?
3. How do we handle absolute value equations?
4. What are some other methods to solve quadratic equations?
5. Can this problem be solved by expanding and factoring instead?

**Tip:** When taking square roots, always remember the "±" to account for both the positive and negative solutions.

Learn how to solve the equation (2x+5)^2 = 4 with a detailed step-by-step solution. This problem covers key algebraic concepts such as squaring binomials and using the square root property. Suitable for students in Grades 8-10.

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