Question
Solve the equation by completing the square. If necessary, round to the nearest hundredth.
x² – 18x = 19
(1 point)
Responses
1; 19
1; 19
–1; 19
–1; 19
3; 6
3; 6
–3; 1
To solve the equation x² - 18x = 19 by completing the square, first move the constant term to the other side:
x² - 18x = 19
x² - 18x + ___ = 19 + ___
x² - 18x + 81 = 19 + 81 (Adding and subtracting half of the coefficient of x, which is (18/2)²)
Now the left side can be written as a squared binomial:
(x - 9)² = 100
Take the square root on both sides:
x - 9 = ±√100
x - 9 = ±10
Add 9 to both sides:
x = 9 ± 10
x = 9 + 10 or x = 9 - 10
x = 19 or x = -1
So the solutions are x = 19 or x = -1. Hence, the correct response would be:
1; 19