Let
f(x) = 2x + 7 if x < -2
f(x) = -x^2 - x + 2 if x >= -2
Find the sum of all values of x such that f(x) = -5.
+129850 2x + 7 = -5 -x^2 - x + 2 = -5
2x = -5 - 7 x^2 + x - 2 = 5
2x = -12 x^2 + x = 7 complete the square on x
x = -6 x^2 + x + 1/4 = 7 + 1/4
(x + 1/2)^2 = 29/4 take the positive root
x + 1/2 = sqrt (29)/2
x = (1 + sqrt (29) ) /2
Sum = -6 + (1 + sqrt 29) / 2 = (-11 + sqrt 29) / 2
