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There are two distinct solutions $x$ to the equation $18+5x^2=20x$. If each solution is rounded to the nearest integer, and then these two integers are multiplied together, what is the result?

Jun 11, 2018

In order to answer this question, one must determine what the solutions are to the equation $$18+5x^2=20x$$. Let's do that, shall we?
 $$18+5x^2=20x$$ When solving quadratic equations, it is generally advisable to move all terms to one side of the equation. $$5x^2-20x+18=0$$ This equation is probably best solved with the quadratic formula. $$a=5; b=-20; c=18\\ x_{1,2}=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$$ Now, plug into this equation and find the roots. $$x_{1,2}=\frac{-(-20)\pm\sqrt{(-20)^2-4*5*18}}{2*5}$$ The rest is a matter of simplifying accurately. $$x_{1,2}=\frac{20\pm\sqrt{40}}{10}$$ Generally, there is a need to put radicals into simplest form, but this is not necessary since the question asks for their rounded value. $$x_1\approx3\\ x_2\approx1$$ Let's find the rounded roots' product. $$x_1*x_2=3*1=3$$ This is it!