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
–3; 1
To solve by completing the square, first move the constant term to the other side of the equation:
x² - 18x = 19
x² - 18x + 81 = 19 + 81
x² - 18x + 81 = 100
Now, rewrite the left side as a perfect square:
(x - 9)² = 100
Now take the square root of both sides:
x - 9 = ±√100
x - 9 = ±10
Now solve for x:
x = 9 ± 10
So the possible solutions are x = 19 or x = -1. Therefore, the correct answer is:
1; 19