
A quadratic equation is an equation which can be written in the form ax^{2} + bx + c = 0 where a, b, and c are constants (as opposed to x, which is a variable). To solve an equation such as ax^{2} + bx + c = 0 by factoring, we factor the left side into factors of the form (Dx  E). We may then conclude that x = E / D is a solution to the original equation. Here is an example:
Original Equation: 2x^{2}  5x = 3 Rewritten equation: 2x^{2}  5x  3 = 0 Equation with factored left side: (2x + 1)(x  3) = 0 Solutions to equation: x = ½ or x = 3 
"Completing the Square" is another method of solving ax^{2} + bx + c = 0.
The idea is this: rewrite the equation in the form x^{2} + bx = c;
then add (¼)b^{2} to both sides,
noticing that x^{2} + bx + (¼)b^{2} = (b + ½)^{2},
a perfect square.
Original Equation: 2x^{2}  8x = 10 Rewritten equation: x^{2}  4x = 5 Complete the left side square: x^{2}  4x + 4 = 5 + 4 Equation with factored left side: (x  2)^{2} = 3^{2} Take square root of both sides: x  2 = ± 3 Solutions to equation: x = 5 or x = 1 

