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Find the largest value of $x$ such that $3x^2 + 17x + 15 = 2x^2 + 21x + 12 - 5x^2 + 17x + 34.$

 Jul 3, 2024
 #1
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Alright. First, let's combine all like terms to this horrible mess. We get that

\(6x^{2}-21x-31=0\)

 

Now, we simply apply the quadratic formula and take the smaller root. Using the fomrula, we get

\(x=\frac{21\pm \sqrt{(-21)^{2}-4\cdot 6(-31)}}{2\cdot 6}\)

 

From this monstrosity, we get that

\(x=\frac{\sqrt{1185}+21}{12}\\ x=\frac{-\sqrt{1185}+21}{12}\)

 

Obviously, the first term of x is bigger, so we take that as our answer. 

We find that x is \(x=\frac{\sqrt{1185}+21}{12}\)

 

So our answer is just the biiger root. 

 

Thanks! :)

 

also, 500th answer...woop woop! :)

 Jul 3, 2024
edited by NotThatSmart  Jul 3, 2024

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