Question

(×+17) . (×+5)

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Answer 1

$(x+17).(x+5)\to \\\\ x^2+5x+17x+85=0\to \\\\ x^2+22x+85=0\\\\ a=1;~b=22;~c=85\\\\\\ \Delta=b^2-4ac\to~ \Delta=22^2-4.1.85\to ~\Delta=484-340\to~\boxed{\Delta= 144}\\\\ x' \neq x''\\\\\\ x= \dfrac{-b\pm \sqrt{\Delta} }{2a} \to~~ x= \dfrac{-22\pm \sqrt{144} }{2.1} \to~~ x= \dfrac{-22\pm 12 }{2} \to\\\\\\ x'= \dfrac{-22+ 12 }{2} \to~~ x'= \dfrac{-10 }{2} \to~~ \boxed{x'=-5}\\\\\\ x''= \dfrac{-22- 12 }{2} \to~~ x''= \dfrac{-34 }{2} \to~~ \boxed{x''=-17}\\\\\\\\ \Large\boxed{\boxed{S=\{-17~;~-5 \}}}$