SOLUTION: Two numbers add up to 300. One number is twice the square of the other number. What are the numbers?

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Question 1171534: Two numbers add up to 300. One number is twice the square of the other number. What are the numbers?
Answer by ikleyn(52817) About Me  (Show Source):
You can put this solution on YOUR website!
.

Let x be "the other" number.


Then "one number" is  (300-x).


From the condition, you have this equation

    300 - x = 2x^2.


The standard form is

    2x^2 + x - 300 = 0.


Solve it using the quadratic formula


    x%5B1%2C2%5D = %28-1+%2B-+sqrt%281%5E2+%2B+4%2A2%2A300%29%29%2F%282%2A2%29 = %28-1+%2B-+sqrt%282401%29%29%2F4 = %28-1+%2B-+49%29%2F4



You have two roots, -12.5  and  12.



They produce two solutions.



1)  One solution is this pair:    "one number" is 300-(-12.5) = 312.5; "the other number" is -12.5.


2)  Second solution is this pair: "one number is 12;                   "the other number" is (300-12) = 288.



CHECK.  1)  2x^2 = 2*(-12.5)^2 = 312.5.     ! correct !

        2)  2*12^2 = 288.                   ! correct !

Solved.