Solve the equation by completing the square, if necessary, round to the nearest hundredth
x^2-18x=19
A. 1;19
B.-1;19
C. 3;6
D. -3;1
To solve this equation by completing the square, we need to follow these steps:
1. Move the constant term to the other side of the equation:
x^2 - 18x = 19
x^2 - 18x - 19 = 0
2. To complete the square, take half of the coefficient of x (-18) and square it:
(-18/2)^2 = (-9)^2 = 81
3. Add and subtract this value inside the parentheses:
x^2 - 18x + 81 - 81 - 19 = 0
(x - 9)^2 - 100 = 0
4. Now, solve for x by taking the square root of the other side:
(x - 9)^2 = 100
x - 9 = ±√100
x - 9 = ±10
x = 9 ± 10
This results in two possible solutions:
x = 9 + 10 = 19
x = 9 - 10 = -1
Therefore, the solutions are x = 19 and x = -1, so the answer is B. -1;19.