hi guys swim teacher gone we will do the derivation of quadratic formula from the standard form of any quadratic equation up to this X is equal to negative be positive negative square root of b squared minus 4ac all over 2a so not be nothing again in the dread-nots informally nothing so start aya we have here the standard form ax squared plus BX plus C is equal to 0 now for us to derive the formula or the quadratic formula we need to use completing the square or the process of completing the square so as you can see we have ax squared plus BX plus C is equal to 0 first step on how to do completing the square yes you need to transpose or transfer your constant to the right side of the equation so rewriting this equation you will have ax squared plus BX is equal to negative C then after this one you need to divide the whole equation by the coefficient of your quadratic term which is a so divided by a it will cancel out this one this will give you x squared plus BX over a is equal to negative C over a and then we will do the completing the square term little square we need to get the coefficient of your linear term which is B over a so how to complete the square you will divide this by 2 so that will be B over a times 1/2 or the reciprocal of 2 so that will be B over 2a and then square it you will have B squared over 4a squared so this will be the third term of your left side of the equation and you will add this to the right side of the your equation you will have x squared plus BX over a plus B squared over 4a squared is equal to negative C over a plus B squared over 4a squared since we do or we are done with the completing the square automatically the left side of your equation is already a perfect square trinomial so when we factor out this one you need to express this part in a square binomial and that will be X plus B over 2a but not in a Hawaiian we extracted the square root of x squared as X and the square root of B squared all over 4a squared simply be all over 2a then square both sides x squared this one or this binomial and this part we need to simplify negative C over a plus B squared over 4a squared getting the CD the LCD is 4a squared that is 4a squared divided by E is 4a times negative C that is negative 4ac then 4a squared divided by 4a squared that is 1 times B squared plus B squared so this is your right side of the equation we have B squared minus 4 AC all over 4a squared then next tap not n we will extract the square roots of the equation this will be cancelled out we will have X plus B over 2a is equal to the squared positive negative square root of b squared minus 4ac over 2a because 4a squared is a perfect square then after this one we will transpose B all over 2a to the other side of the equation and that is X is equal to negative B over 2a positive negative square root of b squared minus 4ac over 2a as you can see marisol on the level or minus nonpareils denominator therefore we can combine the numerators as X is equal to negative b positive negative square root of b squared minus 4ac over 2a and now as you can see we already derive the quadratic formula from the standard form of any quadratic equation so that's it if you have any question about this process on how to derive the quadratic formula then comment down below about your enquiries so again I am featured 1 and this is your quadratic formula don't forget to subscribe our YouTube channel thank you