## 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

Subtraction ofgives