 solve the following equations for x = -4    √(-49)x=

The equation involves a square root of a negative number, specifically \(\sqrt{-49}\). The square root of a negative number is not a real number; instead, it is an imaginary number.

\[
\sqrt{-49} = 7i
\]

Given this, the equation becomes:

\[
x = 7i
\]

Since you want the value of \(x\) for \(x = -4\), the equation \(x = 7i\) remains valid as is, and no substitution or further solution for \(x\) is needed. The expression \(x = 7i\) means that \(x\) is an imaginary number.

Would you like more details or have any questions? Here are some related questions you might consider:

1. What are imaginary numbers, and how are they used in mathematics?
2. How do we interpret and solve equations involving complex numbers?
3. What is the difference between real numbers and imaginary numbers?
4. How do you perform arithmetic operations with complex numbers?
5. Can you provide examples of real-world applications where imaginary numbers are used?

**Tip:** Imaginary numbers are represented as \(i\) where \(i = \sqrt{-1}\). They are often used in engineering and physics to solve problems involving waveforms and oscillations.

solve the following equations for x = -4    √(-49)x=

Explore how to solve equations involving imaginary numbers, focusing on the problem √(-49) and the value of x. This guide covers the concept of imaginary numbers, the square root of a negative number, and the use of the imaginary unit i. Ideal for students in Grades 9-12.

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