solve the following by completing the square
x^2+6x=73
To complete the square for the equation x^2 + 6x = 73, we will follow these steps:
1. Move the constant term (i.e., 73) to the other side of the equation:
x^2 + 6x - 73 = 0
2. Now, to complete the square, we need to find the number that when squared and added to both sides of the equation, makes the left side a perfect square trinomial.
To do this, we take half of the coefficient of x (which is 6), square it, and then add it to both sides of the equation:
(x + 3)^2 = 73 + 9
(x + 3)^2 = 82
Therefore, the completed square form of the equation x^2 + 6x - 73 = 0 is (x + 3)^2 = 82.