Complete the square to transform the quadratic equation into the form (x-p)^2=q
x^2-12x-5=7
To complete the square on the quadratic equation x^2 - 12x - 5 = 7, first move the constant term (7) to the other side:
x^2 - 12x - 5 - 7 = 0
x^2 - 12x - 12 = 0
Next, add the square of half of the coefficient of x to both sides. The coefficient of x is -12, so half of it is -6, and its square is 36.
x^2 - 12x + 36 = 24
(x - 6)^2 = 24
So, the equation in the form (x - p)^2 = q is:
(x - 6)^2 = 24