Solve: x² + 18x + 81 = 0. What is the factor form?

(x + 8)²

(x - 9)²

(x + 9)²

(x - 8)²

$x^^{2} + 18 x + 81 = 0$ :

The first term is $x^^{2}$ , so $a = x$ .
The last term is $81$ , so $b^^{2} = 81$ , which means $b = 9$ (we take the positive root since the middle term is positive).
The middle term is $18 x$ . Let's check if it matches $2 ab$ : $2 (x) (9) = 18 x$ . It does.

Therefore, the quadratic expression $x^^{2} + 18 x + 81$ can be factored into $(x + 9)^^{2}$ .

So the factor form of the equation $x^^{2} + 18 x + 81 = 0$ is $(x + 9)^^{2} = 0$ .