Solve the equation by completing the square. If necessary, round to the nearest hundredth.%0D%0A%0D%0Ax² – 18x = 19%0D%0A(1 point)
To solve the equation x² - 18x = 19 by completing the square, follow these steps:
1. Move the constant term to the right side of the equation:
x² - 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 this value to both sides of the equation:
x² - 18x + 81 = 19 + 81
x² - 18x + 81 = 100
4. Rewrite the left side of the equation as a square of a binomial:
(x - 9)² = 100
5. Take the square root of both sides to solve for x:
x - 9 = ±√100
x - 9 = ±10
x = 9 ± 10
6. Solve for both possibilities:
x = 9 + 10 = 19
x = 9 - 10 = -1
Therefore, the solutions to the equation x² - 18x = 19 are x = 19 and x = -1.