Factorizing involves finding a number pair that satisfies two things: when added together, they must have a sum equal to the coefficient of x and the product must be equal to the product of the coefficient of x2 and the constant. If the pair does not satisfy both conditions, you cannot solve the equation using this formula and must employ an alternate formula.
Completing the square involves creating a perfect square trinomial. In this method, the coefficients and the constant are divided by the value of a. An equal amount determined by the value of b is added to both sides of the equation. The equation is first converted to the form ax2 + bx=c then (b/2)2 is added to both sides of the equation. The next step involves factoring where the left side of the equation is factorized into one double root. Square roots are then taken on both sides. The root on the left is then equated to the root on the right hand side of the equal sign. The solution gives two roots since the root gives an answer with a plus or minus sign.
The quadratic formula is probably the simplest of all methods of solving quadratic equations. This is because you plug in the values of the coefficients of x and the constant directly into a verified formula. The quadratic formula is written in the general form. This method of solving quadratic equations also gives two roots, which are the values of x due to the presence of plus and minus signs.
Another method used to solve quadratic equations is with a spreadsheet program. However, this method is also based on the quadratic formula. Columns A, B, C and D are used for the coefficient of x2, coefficient of x, the constant and the solution respectively.