+26 Let \(f(x) = \left\{ \begin{array}{cl} 2x + 7 & \text{if } x < -2, \\ -x^2 - x + 1 & \text{if } x \ge -2. \end{array} \right.\)Find the sum of all values of \(x\) such that \(f(x) = -5.\)
+36916 Just set the equation = to -5
2x+7 = - 5
2x = -12
x = -6 this is the first part of the piecemeal equation and - 6 is less than - 2 so first answer = -6
Now for the second part of the equation
-x^2 -x+1 = - 5
-x^2 -x + 6 = 0
x^2 + x-6 = 0
(x-2)(x+3) = 0 for this x can be = to 2 or -3 (throw out...because this part of the equation is only for x >=2)
so the two possibilities are x = - 6 or 2
