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

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: Find the largest value of x such that 3x^2 + 17x + 15 = 2x^2 + 21x + 12 - 5x^2 + 17x + 34.      Log On


   

Question 1209215: Find the largest value of x such that 3x^2 + 17x + 15 = 2x^2 + 21x + 12 - 5x^2 + 17x + 34.
Answer by ikleyn(52788) About Me  (Show Source):
You can put this solution on YOUR website!
.
Find the largest value of x such that 3x^2 + 17x + 15 = 2x^2 + 21x + 12 - 5x^2 + 17x + 34.
~~~~~~~~~~~~~~~~~~~~~~~~ 

Collect all the terms of the equation in its left side

    3x^2 + 17x + 15 - 2x^2 - 21x - 12 + 5x^2 - 17x - 34 = 0.


Group like terms

    (3x^2 - 2x^2 + 5x^2) + (17x - 21x - 17x) + (15 - 12 - 34).


Combine like terms

    6x^2 - 21x - 31 = 0.


Use the quadratic formula to find the roots

    x%5B1%2C2%5D = %2821+%2B-+sqrt%28%28-21%29%5E2+-+4%2A6%2A%28-31%29%29%29%2F%282%2A6%29 = %2821+%2B-+sqrt%281185%29%29%2F12.


The greatest root is  %2821+%2B+sqrt%281185%29%29%2F12 = 4.618652413  (approximate value).


ANSWER.  The greatest root is  %2821+%2B+sqrt%281185%29%29%2F12, or about 4.618652413  (approximate value).

Solved.