To solve the equation x² – 18x + 81 = 0, we can use the factoring method. Firstly, we need to find two numbers that multiply to 81 and add up to -18.
The factors of 81 are (9, 9), and both of these factors can be combined as follows:
- (-9) and (-9) both add to give -18.
Thus, we can rewrite the equation as:
(x – 9)(x – 9) = 0
Now, applying the zero product property, we set each factor equal to zero:
x – 9 = 0
Solving for x gives us:
x = 9
Therefore, the repeated solution to the equation x² – 18x + 81 = 0 is x = 9.
This means the only value of x that satisfies the equation is 9.