Question 135529
The equation {{{x^2+12x+c=0}}} will have one distinct solution if the discriminant equals zero. In other words, when  {{{b^2-4ac=0}}}. 


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



{{{b^2-4ac=0}}} Start with the given equation


{{{(12)^2-4(1)c=0}}} Plug in a=1 and b=12



{{{144-4c=0}}} Square and multiply




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



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



{{{c=(-144)/(-4)}}} 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^2+12x+36=0}}} will have one distinct solution