There are different ways to solve a quadratic equation, the main ones that i'm thinking about right now are:
1) factor the equation as a product:
ex: x^2+ 4x + 3 =0
(x+3) (x+1) = 0
x=-3 and x=-1 are the solutions.
To find (x+p) and (x+q) you have to think that (p+q )have to be equal to the number that is multiplied by x, in my example it was 4 (3+1=4), (p times q) have to be equal to the last number of the quadratic equation, the one that is not multiplied by any x, that in my example is 3 (3 x 1= 3)

2) The other way to solve a quadratic function is by using a formula:
given: ax^2 +bx +c=0
x= (-b +/- √(b^2 - 4ac)) / 2a

ex: 3x^2 + 4x -2=0
x= (-4 +/- √16-4(3)(-2)) / 6= (-4 +/- √16+24)/6= (-4 +/- √40) / 6
now there are 2 possibilities: x= (-4+√40) /6
and
x= (-4 - √40) / 6
I hope the examples were clear enough also if i did't get very nice numbers. Look closely to the sings + and -, they are very important

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3 years ago