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Hi,
As to 'solving' Quadratic Equations of the form y = ax^2 + bx + c
Finding x such that y = 0 can be done either by:
1)factoring (showing using quadratic formula naturally has the same results)
ex: x^2 -2x - 3 = 0 factors to (x-3)(x+1)=0 with x = 3 or x = -1
x-= -1 or x = 3
2) When factoring does not seem to work for us, the Quadratic formula always will