SOLUTION: For what value of c will the equation {{{x^2+12x+c=0}}} have one distinct solution?

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Question 135529: For what value of c will the equation x%5E2%2B12x%2Bc=0 have one distinct solution?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
The equation x%5E2%2B12x%2Bc=0 will have one distinct solution if the discriminant equals zero. In other words, when b%5E2-4ac=0.

Notice how a=1, b=12, and c=c


b%5E2-4ac=0 Start with the given equation

%2812%29%5E2-4%281%29c=0 Plug in a=1 and b=12


144-4c=0 Square and multiply



-4c=0-144Subtract 144 from both sides


-4c=-144 Combine like terms on the right side


c=%28-144%29%2F%28-4%29 Divide both sides by -4 to isolate c



c=36 Divide

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Answer:
So our answer is c=36



So the equation x%5E2%2B12x%2B36=0 will have one distinct solution