+866 Find the largest value of $x$ such that $3x^2 + 17x + 15 = 2x^2 + 21x + 12 - 5x^2 + 17x + 34.$
+1588 Absolutely, I’ve been improving my problem-solving abilities in quadratic equations. Let's find the largest value of x such that: 3x2+17x+15=2x2+21x+12−5x2+17x+34
We can solve the equation by combining like terms, moving terms to one side of the equation, and using the quadratic formula.
Steps to solve: 1. Combine like terms: 3x2+17x+15=−3x2+38x+46
2. Move terms to one side: 6x2−21x−31=0
3. Use the quadratic formula: x=2a−b±b2−4ac where a, b, and c are the coefficients of the quadratic equation. In this case, a = 6, b = -21, and c = -31. Substituting these values into the formula, we get:
x=2⋅6+21±(−21)2−4⋅6⋅−31
4. Simplify: x=1221±1185
Since the discriminant (the part under the radical) is positive, there are two real solutions. However, the question asks for the largest value of x. The larger solution will be the one with the positive square root.
Answer: x=121185+21
