The image contains the following equation:

$(4x + 7)^2 = 0$

To solve this equation, we'll take the square root of both sides.

Step 1: Take the square root of both sides.

Since the square of a number is zero only if the number itself is zero, we can write: $4x + 7 = 0$

Step 2: Solve the equation for $x$.

Subtract 7 from both sides: $4x = -7$ Now, divide both sides by 4: $x = -\frac{7}{4}$

Final Answer:

The solution to the equation is: $x = -\frac{7}{4}$

Would you like any additional details or have any questions?

Here are some related questions you might find interesting:

1. What does it mean geometrically when a quadratic equation has a double root?
2. How do you solve quadratic equations by completing the square?
3. What are the steps to solve a quadratic equation by factoring?
4. Can quadratic equations have complex roots, and how are they determined?
5. How can you check your solution to a quadratic equation?

Tip: When solving an equation of the form $(ax + b)^2 = 0$, remember that the equation only has one solution because the square of any real number is non-negative, so it equals zero only when the base is zero.