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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 26, 2024
 #1
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First, let's combine all our like terms and move all the terms to oneside. We get

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

 

Now, we use the quadratic equation. We get that

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

 

Simplifying furher. We get 2 values for x We get

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

 

Clearly, the first value of x is greater in this case, so we have

\(x=\frac{\sqrt{1185}+21}{12}\) as our final anwer. 

 

Thanks! :)

 Jun 26, 2024

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