finding inputs given outputs

Question

g(x) = 5x² + 55x − 11; g(x) = 749

what are the inputs given the output of 749

Answer 1

If g(x) = 5x² + 55x − 11 and g(x) = 749 then:

5x² + 55x − 11 = 749 now subtract 749 from both sides to get:

5x² + 55x − 760 = 0 now divide both sides by 5 to get:

x² + 11x − 152 = 0 now factor to get:

(x + 19)(x - 8) = 0 now set each binomial equal too zero to get:

x + 19 = 0 so x = -19

x - 8 = 0 so x = 8

So the inputs are either 8 or -19