To solve the equation x² – 9 = 16 using the zero product property, we first need to rearrange the equation to set it equal to zero.
Start by subtracting 16 from both sides:
x² – 9 – 16 = 0
This simplifies to:
x² – 25 = 0
Now, we can factor the left-hand side. We recognize that x² – 25 is a difference of squares, which can be expressed as:
(x – 5)(x + 5) = 0
Now, according to the zero product property, if the product of two factors is zero, at least one of the factors must be zero. This gives us two equations to solve:
- x – 5 = 0
- x + 5 = 0
Solving these equations separately:
- For x – 5 = 0, we add 5 to both sides:
- For x + 5 = 0, we subtract 5 from both sides:
x = 5
x = -5
Thus, the solutions to the equation x² – 9 = 16 are:
- x = 5
- x = -5