SOLUTION: Please help so i can learn how to do this! I would really appreciate it........ If twice the square of a positive number is added to the product of -9 and the number, the result is

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Question 862365: Please help so i can learn how to do this! I would really appreciate it........ If twice the square of a positive number is added to the product of -9 and the number, the result is 18. Find the number
Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website!
let x = the positive number.
twice the square of the positive number is therefore equal to 2*x^2.
the product of -9 and the number is equal to -9*x
if you add twice the square of the positive number to the product of -9 and the number, the result is 18.
this becomes:
2*x^2 + -9*x = 18 which simplifies to:
2*x^2 - 9*x = 18
this is a quadratic equation.
convert it to standard form by subtracting 18 from both sides of the equation to get:
2x^2 - 9x - 18 = 0
factor this equation to get:
(2x + 3) * (x - 6) = 0
either one of these factors or both have to be equal to 0.
set each factor equal to 0.
2x + 3 = 0 results in x = -3/2
x - 6 = 0 results in x = 6
since the number has to be positive, x = 6 is the number.
2 * 6^2 = 2*36 = 72
-9 * 6 = -54
72 - 54 = 18
the solution is confirmed to be good because the original problem statement is true when x is replaced with 6.
here's a reference you might find helpful.
http://www.purplemath.com/modules/translat.htm