SOLUTION: x� + 12x + 11 I'm assuming you meant: x� + 12x + 11 = 0 (Yes, the zero matters ;-)

Question 619309: x� + 12x + 11
I'm assuming you meant:
x� + 12x + 11 = 0 (Yes, the zero matters ;-)
Answer by mathsmiles(68) (Show Source): You can put this solution on YOUR website!
x� + 12x + 11 = 0
(x + ...) (x + ... ) = 0
We need to find two factors of 11 whose sum is 12. That's rather easy since 11 is prime. It's only factors are 1 and itself - 11.
(x + 11)(x + 1) = 0
Now solve each of these separately. That is, at least one of these two factors must be zero for the whole equation to be equal to zero.
(x+11) = 0
Subtract 11 from both sides ...
x = -11
Now the other ...
x+1 = 0
Subtract 1 from both sides ...
x = -1
So both -11 and -1 are possible solutions for x. Let's check ...
x� + 12x + 11 = 0
(-11)^2 + 12(-11) + 11 = 0
121 - 132 + 11 = 0
0 = 0 Check!
x� + 12x + 11 = 0
(-1)^2 + 12(-1) + 11 = 0
1 - 12 + 11 = 0
0 = 0 Check!
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