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Show proof of deriving the Quadratic Formula from the Quadratic Equation ax^2 + bx + c = O

  • Maths -

    factor out an a
    a(x^2 + b/a) + c = 0

    compete the square and don't change the value
    a(x^2 + b/a + b^2/4a^2) - a(b^2/4a^2) + c = 0

    a(x + b/2a)^2 - b^2/4a + c = 0
    (x + b/2a)^2 - b^2/4a^2 + c/a = 0
    (x+b/2a)^2 = (b^2 - 4ac)/4a^2
    x + b/2a = ±√(b^2-4ac) / 2a
    x = (-b ± √(b^2-4ac))/2a

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