# How do you solve x^2 + 3x - 14 <= 14?

Jun 11, 2015

Solve quadratic inequality:$f \left(x\right) = {x}^{2} + 3 x - 28 \le 0$

#### Explanation:

First solve f(x) = 0 by the new Transforming Method.
Factor pairs of -28. Roots have different signs
Proceed: (--2, 14)(-4, 7). This sum is 3 = b. Therefor, the 2 real roots are the opposite: x = 4 and x = -7.

Next, plot (-7) and (4) on a number line. The parabola opens upward (a > 0), then, between the 2 x-intercepts,$f \left(x\right) \le 0.$

Answer by closed interval: [-7, 4]
Graph:

----------------|0---------|-7=========|0=======|4----------------