Finding the largest $c$ such that $4.7(x-c) = 9-\frac12x^2$ has a real solution $x$

algebra-precalculus inequality quadratics

There are two ways:

  • compute the discriminant of the quadratic trinomial and find the largest $c$ that makes it non-negative;

  • express $c$ as a function of $x$, and find the global maximum.

There is no largest $c$.

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