SOLUTION: Six times the square of the difference between a number and 5 is -96. Find the numbers.

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Question 1131031: Six times the square of the difference between a number and 5 is -96. Find the numbers.
Found 2 solutions by ankor@dixie-net.com, ikleyn:
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Six times the square of the difference between a number and 5 is -96. Find the numbers.
:
6%28x-5%29%5E2+=+-96
simplify, divide both sides by 6, then FOIL (x-5)(x-5)
x^2 - 10x + 25 = -16
x^2 - 10x + 25 - 16 = 0
x^2 - 10x + 9 = 0
Factors to
(x-9)(x-1) = 0
Two apparent solutions
x = 9
x = 1
But actually there is no solution
try both solutions in the original equation
6%289-5%29%5E2 =
6(4)^2 =
6(16) = +96, not a solution
6%281-5%29%5E2 =
6(-4)^2 =
6(16) = + 96, not a solution either



Answer by ikleyn(52893) About Me  (Show Source):
You can put this solution on YOUR website!
.
There is NO and CAN NOT be a solution in real numbers under such conditions.

Because the square of a real number is NEVER negative.


Totally obvious.