Deriving the Quadratic Formula
Quadratic equations take the form(1) withAny equation of this form may be solved using the formulaThis formula is proved by completing the square for (1).
Starting fromdivide through by a to give(2) then write
Substitute this into (2) to give
Now make x the subject. Start by moving the last two terms to the right hand side.
Collect the terms on the right by adding them as fractions.
Square root both sides to give