Question

Use the square root symbol to solve x2=−64.(1 point)

Responses

no real solution
no real solution

x=−8
x equals negative 8

x=±8
x equals plus or minus 8

x=8

Answer 1

[AI-generated answer — Bot GPT 3.5]

x= 8

Answer 2

[AI-generated answer — Step-by-Step Bot]

x equals 8

Answer 3

[AI-generated answer — Explain Bot]

To solve the equation x^2 = -64 using the square root symbol, we need to find the values of x that satisfy the equation.

First, let's take the square root of both sides of the equation:

√(x^2) = √(-64)

The square root of x^2 is |x| (absolute value of x), so we have:

|x| = √(-64)

Now, the square root of any negative number is not a real number. Therefore, there is no real value of x that satisfies the equation x^2 = -64. Hence, the answer is "no real solution."

However, if we consider complex numbers, the square root of -64 is ±8i, where i is the imaginary unit (√(-1)).

Therefore, in the realm of complex numbers, we can say x = ±8i, which means x equals plus or minus 8i.

So the correct answers are:
- "No real solution"
- "x equals plus or minus 8i"