Solve x2−64=0

Question

using square roots.(1 point)
Responses

x=1 and x=64
x=1 and x=64

x=8 and x=−8
x=8 and x=−8

x=4 and x=−16
x=4 and x=−16

Answer 1

To solve the equation \( x^2 - 64 = 0 \) using square roots, we start by isolating \( x^2 \):

1. Add 64 to both sides: \[ x^2 = 64 \]

2. Now, take the square root of both sides. Remember that taking the square root can yield both a positive and a negative solution: \[ x = \pm 8 \]

Thus, the solutions are:

\[ x = 8 \quad \text{and} \quad x = -8 \]

The correct response is: x=8 and x=−8.