Some help please, Mike?

x^2 – 12x +k = 0 In this equation, k is a constant. For which values of k does the equation have only one solution? I know I can set the discriminant to zero and solve for k. But is there another way to solve? Thanks!

The equation will have only one solution when it can be simplified to (x-a)^2. If you know your binomial squares really well, you might just see it what k needs to be, but if it doesn’t jump out at you right away, just FOIL: x^2-2ax+a^2

In this case, we know -12x=-2ax, so we can see that x=6. So k must equal 6^2=36

Does that help?

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