where x represents a variable or an unknown, and a, b, and c are constants with a not equal to 0. (If a = 0, the equation is a linear equation.)
The constants a, b, and c are called, respectively, the quadratic coefficient, the linear coefficient and the constant or free term. Quadratic equations can be solved by factoring, completing the square, using the quadratic formula, and graphing.
Here are some examples of a Quadratic Equation:
a) x2+2x-8=0
b) x2+10x-18=0
c) 9x2+4x-13
Solutions
a) x2+2x-8=0 *factor this equation
(x+4)(x-2) *find what must add to become 2x and find the factors of -8
x=-4 , x=2 *subtract 4 to both sides (x+4) , add 2 to both sides (x-2)
b) x2 -10x-18=0 *complete the square
*determine a,b,c (a=1,b=-10,c=-18)
x2 -10x =18 *add 18 to both sides
x2 -10x+25=18+25 *find (b/2)^2 = (-5)^2 or 25
x2 -10x+25=43 *factor
(x-5)(x-5)=43 or (x-5)^2=43 *square both sides
x-5 = ±43^(1/2) *add 5 to both sides x = 5±43^(1/2)
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