Solve the following quadratic equation by completing the square x^2-2x=323
To solve the equation x^2 - 2x = 323 by completing the square, follow these steps:
1. Move the constant term to the right side of the equation:
x^2 - 2x - 323 = 0
2. Take half of the coefficient of x, square it, and add it to both sides:
Dividing -2 by 2 gives -1. Squaring -1 gives 1.
x^2 - 2x + 1 = 323 + 1
x^2 - 2x + 1 = 324
3. Factor the left side of the equation:
(x - 1)^2 = 324
4. Take the square root of both sides:
x - 1 = ±√324
x - 1 = ±18
5. Solve for x:
x = 1 + 18 or x = 1 - 18
x = 19 or x = -17
Therefore, the solutions to the quadratic equation x^2 - 2x = 323 are x = 19 and x = -17.