Recall that not matter what kind of solutions the quadratic equation may have, we can always complete the square. We can use this to derive a general formula for solving a quadratic equation. Let's consider the standard form of a general quadratic equation.
ax^2+bx+c = 0
The first thing we need to do is to isolate the terms containing x. Then we can divide by a so that the leading coefficient becomes 1.
To complete the square we should add the square of half the value of the linear term to obtain a perfect square trinomial. After doing this we can factor the perfect square trinomial as a squared binomial and proceed by calculating the square root of both sides.
Let's recall the definition of absolute value of a quantity.
|a| = a if a > 0 - a if a <0
Notice that considering |a| in ± sqrt(b^()2-4ac)2|a| implies leaving the signs in front of the fraction just like they are or swapping them. However, it is the same to have ± or ∓, since this only indicates that there are two possible solutions. The order does not matter. Hence, we can replace |a| with a without problems.
