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There are two distinct solutions x to the equation 18 + 5x^2 = 30x. If each solution is rounded to the nearest integer, and then these two integers are multiplied together, what is the result?

 Apr 6, 2021
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Moving all the terms to the left side and arranging gives $5x^2+30x+18=0$

 

Using the quadratic formula, you get $x=\frac{-30+\sqrt{30^2-4(18)(5)}}{2(5)}$ and $x=\frac{-30-\sqrt{30^2-4(18)(5)}}{2(5)}$, which simplifies to

 

$x=-3+\frac{3\sqrt{15}}{5}$ and $x=-3-\frac{3\sqrt{15}}{5}$.

 

When rounded, these give $x=-3+2=-1$ and $x=-3-2=-5$.

 

When multiplied, these give $-1*-5=\boxed{5}$

 Apr 6, 2021

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