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# Help!

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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

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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!
Jun 12, 2018
edited by TheXSquaredFactor  Jun 12, 2018