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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?

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

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