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.
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