To solve the equation x² – 18x + 81 = 0, we can factor the quadratic. First, we need to identify two numbers that multiply to 81 (the constant term) and add up to -18 (the coefficient of x).
In this case, the numbers -9 and -9 satisfy these conditions, since:
- -9 × -9 = 81
- -9 + -9 = -18
Thus, we can rewrite the equation as:
(x – 9)(x – 9) = 0 or simply (x – 9)² = 0.
Now, we set the factor equal to zero:
x – 9 = 0
Solving for x, we find:
x = 9.
Therefore, the value of x that makes the equation true is x = 9.