A quadratic equation is an equation which can be written in the form ax2 + bx + c = 0 where a, b, and c are constants (as opposed to x, which is a variable). To solve an equation such as ax2 + 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: 2x2 - 5x = 3
Re-written equation: 2x2 - 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 ax2 + bx + c = 0.
The idea is this: re-write the equation in the form x2 + bx = c;
then add (¼)b2 to both sides, noticing that x2 + bx + (¼)b2 = (b + ½)2, a perfect square.
Original Equation: 2x2 - 8x = 10
Re-written equation: x2 - 4x = 5
Complete the left side square: x2 - 4x + 4 = 5 + 4
Equation with factored left side: (x - 2)2 = 32
Take square root of both sides: x - 2 = ± 3
Solutions to equation: x = 5 or x = -1