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

 Jun 1, 2024
 #1
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deleted

 Jun 1, 2024
edited by Bosco  Jun 1, 2024
 #2
avatar+806 
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First off, let's combine some like terms and move all terms to one side. 

 

We get \(6x^{2}-21x-31=0\). Unfortunately, this can't be factored without radicals, so let's use the Qudratic Formula. 

 

We get \(x=\frac{21\pm \sqrt{(-21)^{2}-4\cdot 6(-31)}}{2\cdot 6}\). Simplifying, we get 

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

 

We want to take the biggest value of x we could, which would be \(x=\frac{\sqrt{1185}+21}{12}\)

 

Thanks! :)

 Jun 1, 2024

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