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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 $$f(x) = -5.$$

May 8, 2021

#1
+32859
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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

May 8, 2021