Which is easier? completing the square or quadratic formula explain

the quadratic formula is derived by completing the square

in other words, by using the quadratic formula, you do complete the square but you skip straight to the answer

below is the derivation of the quadratic formula just for fun

note: I used the method of completing the square to derive the formula

ax²+bx+c=0

group like terms

(ax²+bx)+c=0

factor out quadratic coefient

take 1/2 of linear coefient and square it

(b/a)/2=b/(2a), ((b/(2a))^2=(b^2)/(4a^2)

add positive and negative of it inside parntheasees

factor perfect square trinomial

expand

add (b^2/4a-c) to both sides

divide by both sides by a

before we go on, combine right side into 1 fraction

(c/a)(4a/4a)=4ac/4a^2, so

square root both sides

subtract from both sides

in conclusion, the quadratic formula completes the square for you and is therefore faster when you are given the function in standard form (0=ax²+bx+c).

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step-by-step explanation: