+713 Find the largest value of $x$ such that $3x^2 + 17x + 15 = 2x^2 + 21x + 12 - 5x^2 + 17x + 34.$
+1365 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! :)
