Please help
Solve the following quadratic equation by completing the square x^ - 2x = 323 can you show me the steps please
Sure! Here are the steps to solve the quadratic equation x^2 - 2x = 323 by completing the square:
1. Move the constant term to the right side of the equation:
x^2 - 2x = 323
x^2 - 2x - 323 = 0
2. To complete the square, find the value that needs to be added and subtracted to make the left side a perfect square trinomial. The formula is (b/2)^2 where b is the coefficient of the linear term:
b = -2
(-2/2)^2 = (-1)^2 = 1
3. Add and subtract 1 inside the parentheses:
x^2 - 2x + 1 - 1 = 323
4. Rewrite the equation as a perfect square trinomial:
(x - 1)^2 - 1 = 323
5. Add 1 to both sides of the equation:
(x - 1)^2 = 324
6. Take the square root of both sides:
x - 1 = ±√324
x - 1 = ±18
7. Solve for x by adding 1 to both sides:
x = 1 ± 18
Therefore, the solutions to the quadratic equation x^2 - 2x = 323 are x = 1 + 18 = 19 and x = 1 - 18 = -17.