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the quadratic formula is really complex.

so, if you can avoid it, you should.

one way i do this is by getting the trinomial into

X^2 - 2YX + Y^2 = 0 form.

here's an example

lets say we have

x^2 - 2x - 5 = 0

normally we would have to do the quadratic formula

however, if we get it into this form, we can get

x^2 - 2(1)x + 1 = 6

all i did was add 6 to both sides of the equation.

you can now simplify the left side of the equation, and be left with

(x-1)^(2) = 6

to get ride of the exponent on the left side, find the square root of both sides.

this will leave you with

(x-1) = (+ or -)radical(6)

add one to both sides and you will get

x = 1 (+ or -)radical(6)

therefore,

x can equal 1 + radical(6)

or 1 - radical(6)

now, this may seem complex, but it is easy once you get used to it. It is far more efficient than the long quadratic formula.

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