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, we can follow these steps:
1. Move the constant term to the right side of the equation:
x² – 18x - 19 = 0
2. Take half of the coefficient of x and square it:
(-18/2)^2 = 81
3. Add the result from step 2 to both sides of the equation:
x² – 18x + 81 = 19 + 81
x² – 18x + 81 = 100
4. Factor the perfect square trinomial on the left side:
(x - 9)(x - 9) = 100
5. Take the square root of both sides:
√((x - 9)(x - 9)) = ±√100
(x - 9) = ±10
6. Solve for x:
x - 9 = 10 or x - 9 = -10
x = 10 + 9 or x = -10 + 9
x = 19 or x = -1
Therefore, the solutions to the equation x² – 18x = 19 are x = 19 and x = -1.
Answer: –1; 19