# How do you solve #14 x ^2+ 57x + 28 = 0#?

##### 2 Answers

#### Explanation:

(1) For

Now

(2) Factoring can also be done as follows:

(3) Completing the square can be done as follows. Note that

As above,

Solve:

Ans

#### Explanation:

I use the new Transforming Method (Socratic Search)

Transformed equation:

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.