For which of the following equations are x = 5 and x = -5 both solutions?

To find the equations for which both x = 5 and x = -5 are solutions, we need to understand that both values need to satisfy the same equation.

One way to form such an equation is to use the fact that if x = 5 and x = -5 are roots, the factors of the equation can be represented as:

• (x – 5)
• (x + 5)

This leads us to the equation:

(x – 5)(x + 5) = 0

Expanding this gives:

x² – 25 = 0

This shows that any equation that can be derived from (x – 5)(x + 5) = 0 or equivalent forms will have both x = 5 and x = -5 as solutions. Therefore, equations like:

• x² – 25 = 0
• 2x² – 50 = 0 (scaled version)
• x² + 10x – 15 = 0 (if roots are modified accordingly)

will also be valid. It’s critical that both solutions satisfy the same polynomial equation for them to be classified as solutions of that equation.