Complete the square x^2+14x-y+42=0
To complete the square for the quadratic equation x^2 + 14x - y + 42 = 0, we will only focus on the terms that involve x.
First, we move the constant term (42) to the other side of the equation:
x^2 + 14x - y = -42
Next, we take half of the coefficient of x (which is 14) and square it to add and subtract to the equation:
x^2 + 14x + (14/2)^2 - (14/2)^2 - y = -42
x^2 + 14x + 49 - 49 - y = -42
(x + 7)^2 - 49 - y = -42
Now, simplifying:
(x + 7)^2 - y = 7
Therefore, the completed square form of the equation x^2 + 14x - y + 42 = 0 is:
(x + 7)^2 - y = 7