This (arguably unhelpful) phrase seems to be taught across schools all over the world. What are some other phrases like this that are common ?

  • Caveman
    3•1 month ago
    • ax^2 + bx + c = 0
    • ax^2 + bx = -c move the c over
    • x^2 + (b/a)x = -c/a divide by a
    • x^2 + (b/a)x +(b/2a)^2 = -c/a + (b/2a)^2 complete the square
    • (x + b/2a)^2 = -c/a + (b/2a)^2 factor the left hand side
    • x + b/2a = sqrt(-c/a + (b/2a)^2) now we just tidy it up
    • x = -b/2a + sqrt(-c/a + b2/4a2)
    • x = -b/2a + (2a/2a) sqrt(-c/a + b2/4a2)
    • x = (-b + (2a)sqrt(-c/a + b2/4a2))/2a
    • x = (-b + sqrt(-4ac + b^2))/2a move 2a into the square root and multiply it with what’s inside

    The derivation of the quadratic formula is nice because it doesn’t rely on anything fancy and it’s all tricks the teacher is likely to teach around the same time you’re learning it. It’s not voodoo shit, it’s just the ax^2 + bx + c = 0 and you solve for x.

    • JWBananasEnglish
      1•1 month ago

      Thanks for the alternative explanation. Completing the square never made much sense to me either, so I never would have arrived there.