Answer
1. Factoring, and then applying the zero product rule.
2. Completing the square.
3. Using the quadratic formula.
Most people choose the quadratic formula.
(discussion in step-by-step)
Work Step by Step
1. Factoring, and applying the zero product rule.
2. Completing the square.
3. Using the quadratic formula.
Preferred (depends from person to person)
1. One may prefer this method to avoid square roots and multiplication needed by the quadratic formula.
But, sometimes, factors such as $(x-1+\sqrt{3}$) will not be obvious to find. The method is good, fast and reliable when the trinomial is reducible over the set of integers.
2. Same logic as in case 1. But, if the coefficients are fractions, the work may become tedious.
3. This method is preferred by most because you have steps that ensure that
- you know whether there are real solutions and if they are differrent or repeated.
- Once you know (discriminant $b^{2}-4ac$ is positive or zero$)$
that there are real solutions,
applying the formula $x=\displaystyle \frac{-b\pm\sqrt{b^{2}-4ac}}{2a}$ is a sure way to obtain the results.
It might be the most tedious to some, but most people choose (3) as their preferred method.
