Question

What is the solution to X^2–64=0

Answer 1

x = 8, x = -8

Explanation:

Hello!

We can use the Difference of Squares Formula:
`(a + b)(a - b) = a^2 - b^2`

We need the two terms to be perfect squares for this formula to work, and subtraction has to be the operation. As you can see x² is a square of x, and 64 is the square of 8.

Solve:

• x² - 64 = 0
• (x + 8)(x - 8) = 0

Set each factor to zero. (Zero Product Property)

• x + 8 = 0
• x = -8

And

• x - 8 = 0
• x = 8

The solutions are x = 8, and x = -8.