Use the method of completing the square to transform the quadratic equation into the equation form (x + p)^2 = q. 6+12x+3x^2=0
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The cost of cable (c) in terms of months (m) is
c = (49.99 +9.95 +9.95 -10.00)m
c = 59.89m
The cost of satellite TV (s) in terms of months is
s = 125.00 +49.95m
The difference in price is ...
s - c = (125 +49.95m) -(59.89m)
s - c = 125 -9.94m
At 12 months, the difference in price is
s - c = 125 -9.94*12 = 5.72
This number is positive, which means ...
the Cable company will save Margot money over a 12-month period.
At 24 months, the difference in price is
s - c = 125 -9.94*24 = -113.56
This number is negative, which means ...
the Satellite TV company will save Margot money over a 24-month period.
_____
A graph of the costs shows a cross-over at 12.5 months. Until then, the Cable provider is less expensive. Over terms longer than that, the Satellite TV provider is less expensive.
c = (49.99 +9.95 +9.95 -10.00)m
c = 59.89m
The cost of satellite TV (s) in terms of months is
s = 125.00 +49.95m
The difference in price is ...
s - c = (125 +49.95m) -(59.89m)
s - c = 125 -9.94m
At 12 months, the difference in price is
s - c = 125 -9.94*12 = 5.72
This number is positive, which means ...
the Cable company will save Margot money over a 12-month period.
At 24 months, the difference in price is
s - c = 125 -9.94*24 = -113.56
This number is negative, which means ...
the Satellite TV company will save Margot money over a 24-month period.
_____
A graph of the costs shows a cross-over at 12.5 months. Until then, the Cable provider is less expensive. Over terms longer than that, the Satellite TV provider is less expensive.