https://file.aiquickdraw.com/mathbot/file/1725292783924ntsx7lvf.jpg

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.

Learn how to solve the quadratic equation (4x + 7)^2 = 0 step-by-step. This problem involves using the quadratic equation formula and understanding square roots in algebra. Suitable for students in Grades 9-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation