Solve the equation by completing the square. If necessary, round to the nearest hundredth.

x² – 18x = 19
A. 1; 19
B. –1; 19
C. 3; 6
D. –3; 1

1 answer

First, we need to move the constant over to the right side:

x² – 18x + _____ = 19 + _____

To figure out what goes in the blank, we take half of the coefficient of x (-18) and square it:

(-18/2)² = 81

So we add 81 to both sides:

x² – 18x + 81 = 100

Now we can write the left side as a square:

(x – 9)² = 100

Taking the square root of both sides, we get:

x – 9 = ±10

Adding 9 to both sides:

x = 9 ± 10

So the solutions are:

x = 19 or x = –1

Therefore, the answer is B. –1; 19.