Question

Find the solutions to x² - 64 = 0. Enter your answers separated by commas.

Answer 1

x = 6, -6

Step-by-step explanation:

`{x}^(2) - 64 = 0 \\ add \: 64to \: both \: sides \: of \: the \: equation \\ {x}^(2) - 64 + 64 = 64 \\ {x}^(2) = 64 \\ take \: the \: square \: root \: of \: both \: sides \\ \sqrt{ {x}^(2) } = √(64) \\ x = 6 \: and \: - 6`

Answer 2

The equation x² - 64 = 0 is a difference of squares and factors into (x + 8)(x - 8) = 0; the solutions are -8, 8.

Step-by-step explanation:

To find the solutions to x² - 64 = 0, we can recognize that this is a difference of squares. This equation factors into (x + 8)(x - 8) = 0. Setting each factor equal to zero gives us the solutions:

• x + 8 = 0 → x = -8
• x - 8 = 0 → x = 8

Therefore, the solutions to the equation are -8, 8.