Solve the equation by completing the square. If necessary, round to the nearest hundredth.
x² – 18x = 19
To complete the square for the quadratic equation x² - 18x = 19, we need to add and subtract (18/2)² to both sides of the equation:
x² - 18x + (18/2)² = 19 + (18/2)²
x² - 18x + 81 = 19 + 81
x² - 18x + 81 = 100
Now, we can rewrite the left side of the equation as a perfect square:
(x - 9)² = 100
Now, take the square root of both sides:
x - 9 = ±√100
x - 9 = ±10
Add 9 to both sides to solve for x:
x = 9 ± 10
This gives you two possible solutions:
x = 9 + 10 = 19
x = 9 - 10 = -1
Therefore, the solutions to the equation x² - 18x = 19 are x = 19 and x = -1.