SOLUTION: when the cube of a number is added to twice its square, the result is equal to 18 more than 9 times the number

Question 408103: when the cube of a number is added to twice its square, the result is equal to 18 more than 9 times the number
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
when the cube of a number is added to twice its square,
the result is equal to 18 more than 9 times the number
:
x^3 + 2x^2 = 9x + 18
x^3 + 2x^2 - 9x - 18 = 0
Factor by grouping
x^2(x + 2) - 9(x + 2)
Factor out (x+2) and you have:
(x^2 - 9)(x + 2) = 0
x = -2
and
x^2 - 9 = 0
difference of squares
(x-3)(x+3) = 0
x = 3
x = -3
:
Check all three solutions in original equation
x^3 + 2x^2 = 9x + 18
x=-2
(-2)^3 + 2(-2)^2 = 9(-2) + 18
-8 + 8 = -18 + 18; a good solution
:
x=3
3^3 + 2(3^2) = 9(3) + 18
27 + 18 = 27 + 18; a good solution
:
(-3)^3 + 2(-3^2) = 9(-3) + 18
-27 + 18 = -27 + 18; a good solution also
:
we can say, x = -2, -3, +3, are all solutions of x

RELATED QUESTIONS
When 10 is added to the square of a positive number, the result is equal to three times... (answered by lwsshak3)

when 80 of a number is added to 10 the result is 14 more than 20% of twice the... (answered by Fombitz)

When 80% of a number is added to 10 the result is 14 more than 20% of twice the... (answered by MathLover1)

when 100 is added to a number, the result is 50 more than 3 times the number. find the... (answered by josgarithmetic)

When 100 is added to a number the, result is 50 more than 3 times the number. Find the... (answered by josgarithmetic)

When 100 is added to a number, the result is 50 more than 3 times the number. Find the... (answered by Alan3354,ikleyn)

when 100 is added to a number,the result is 50 more than 3 times the number. find the... (answered by ikleyn,rauf.gour@gmail.com)

When a number is added to six times its square, the result is 12. Find the... (answered by solver91311)

if a number is added to twice its square, the result is 6. find the... (answered by Earlsdon)