Solve the following quadratic equation by completing the square.
x^2 - 2x = 323
To solve this quadratic equation by completing the square, we first need to move the constant term to the other side of the equation:
x^2 - 2x = 323
x^2 - 2x - 323 = 0
Next, we'll complete the square by taking half of the coefficient of the x-term (-2) and squaring it:
(-2/2)^2 = 1
Now, we add and subtract this value inside the parenthesis:
x^2 - 2x + 1 - 1 - 323 = 0
(x - 1)^2 - 324 = 0
Now, we can write the perfect square trinomial as (x - 1) multiplied by itself:
(x - 1)^2 = 324
Take the square root of both sides to solve for x:
x - 1 = ±√324
x - 1 = ±18
Now we have two possibilities for x:
x - 1 = 18 or x - 1 = -18
Solving for x in the first equation:
x = 18 + 1
x = 19
Solving for x in the second equation:
x = -18 + 1
x = -17
Therefore, the solutions to the quadratic equation x^2 - 2x = 323 are x = 19 and x = -17.