Question 1042347: help: The product of a negative number and 14 more than seven times the number is 105. Find the two numbers. Found 2 solutions by jorel555, Theo:Answer by jorel555(1290) (Show Source):
You can put this solution on YOUR website! Let n be your number. Then:
n(7n+14)=105
7nē+14n-105=0
nē+2n-15=0
(n+5)(n-3)=0
n=-5 or 3
If n=-5, then 7n+14=-21.☺☺☺☺
your formula is x * (7x + 14) = 105
simplify to get 7x^2 + 14x = 105
subtract 105 from both sides to get 7x^2 + 14x - 105 = 0
factor to get(7x+35) * (x-3) = 0
solve for x to get x = -5 or x = 3
confirm by replacing x in the original equation to see if the equation holds true.
original equation is x * (7x + 14) = 105
when x = -5, this becomes -5 * (-35 + 14) = 105 which becomes -5 * -21 which becomes 105 = 105.
when x = 3, this becomes 3 * (21 + 14) = 105 which becomes 3 * 35 = 105 which becomes 105 = 105.
both values of x makes the original equation true, but your answer has to be -5 because you are looking for a negative number.
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