How do you solve #14 x ^2+ 57x + 28 = 0#?
(2) Factoring can also be done as follows:
(3) Completing the square can be done as follows. Note that
I use the new Transforming Method (Socratic Search)
Both roots are negative. Factor pairs of (392) --> (-2, -196)(-4, -98)(-8, -49). This sum is -57 = -b. Then the 2 real roots of (2) are: -8 and -49.
Therefor, the 2 real roots of original equation (1) are:
NOTE . Solving by this Transforming Method is simpler and faster because it avoids the lengthy factoring by grouping, or the boring computation with the formula. In addition, it avoids solving the 2 binomials.