22One solution, discriminant=0

For what value of $\displaystyle c$ does $\displaystyle x^2 + 12x + c = 0$ have exactly one real solution?

c = 36 is the value that gives exactly one real solution. Setting the discriminant 12² − 4(1)(c) to zero gives 144 − 4c = 0, so c = 36. Checking: x² + 12x + 36 = (x+6)², a perfect square with one repeated root.