Just to preface: quadratic equations take the form ax^2 + bx + c. (Did you mean x^2 - 12x + 7)?
First, move the c term to the right side of the equation:
x^2 - 12x = -7
Then, calculate (b/2)^2:
(-12/2)^2 = (-6)^2 = 36
Now add 36 to both sides:
x^2 - 12x + 36 = 7 + 36
x^2 - 12x + 36 = 43
Now factor the left side:
(x + 6)^2 = 43
And solve algebraically. sqrt = square root
sqrt (x + 6)^2 = +/- sqrt43
x + 6 = +/- sqrt43
x = +/- sqrt43 - 6, or
x = -6 + sqrt43, -6 - sqrt43
