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I was working with inequalities and came across this question, I have underlined the step which I don't understand.

It goes like this, $$4x^2-64x+249≥0$$ Implies, $$x^2-64x+\frac{249}{4}≥0$$

I approached my teacher thinking it was a typo but he told me it was not.

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    $\begingroup$ It is a typo: it should be $-16x$, not $-64x$ $\endgroup$
    – A. Goodier
    Apr 26, 2020 at 9:28
  • $\begingroup$ @A.Goodier, that's what I was thinking but teacher declined and Alex me to follow the next step $\endgroup$
    – Arjun
    Apr 26, 2020 at 9:30
  • $\begingroup$ As written, the implication is false, e.g. take $x=10$ $\endgroup$
    – A. Goodier
    Apr 26, 2020 at 9:33

1 Answer 1

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It should be $16x$ and this is a typo. This claim is substantiated by what is done in the next step: $$(x-8)^2+\frac{249}{4}-64=x^2-16x+\frac{249}{4}$$ which is what you have in mind as well.

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