Solve the equation by completing the square: Z ^2- 2z = 323
To solve the equation by completing the square, we first rearrange the equation to have the constant term on one side:
z^2 - 2z = 323
Next, we need to complete the square. To do this, we take half of the coefficient of z (-2) and square it:
(-2/2)^2 = 1
Add this value to both sides of the equation:
z^2 - 2z + 1 = 323 + 1
z^2 - 2z + 1 = 324
Now, the left side of the equation can be factored as a perfect square:
(z - 1)^2 = 324
Take the square root of both sides:
z - 1 = ±√324
z - 1 = ±18
Solve for z:
z = 1 ± 18
z = 1 + 18 or z = 1 - 18
z = 19 or z = -17
Therefore, the solutions to the equation z^2 - 2z = 323 are z = 19 and z = -17.