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Do these answers both work in our original equation? Let's check:

x = 3: x^2 - x - 6 = 0 which gives ( 3 )^2 - ( 3 ) - 6 = 0 which gives 9 - 3 - 6 = 0 ... yep!


x = -2 ... x^2 - x - 6 = 0 which gives ( -2 )^2 - ( -2 ) - 6 = 0 which gives 4 + 2 - 6 = 0 ... yep! ... remember these ( ) guys are really important for negative guys!

They both work, so they are both solutions to the equation. They are really a set of solutions, so we put them together in set brackets:

The official answer is     { -2, 3 }

(No, this is NOT an ( x , y ) point like ( -2, 3 ) .)

Let's do another one:

Solve  x^2 + 3x - 18 = 0

Factor: ( x - 3 ) ( x + 6 ) = 0 ... Blobs = 0: x - 3 = 0 or x + 6 = 0 ... Solve: add 3 to both sides of the first equation and subtract 6 from both sides of the second equation, which gives x = 3 or x = -6

{ -6, 3 }