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    Topics || Problems

    Derivation of Quadratic Formula

    \(a{x^2} + b{y^2} + c = 0\)

    \(\frac{a}{a}{x^2} + \frac{b}{a}x + \frac{c}{a} = 0\) ; Divide both sides by a

    \({x^2} + \frac{b}{a}x = - \frac{c}{a}\)

    \({x^2} + \frac{b}{a}x + {\left( {\frac{b}{{2a}}} \right)^2} = \frac{{ - c}}{a} + {\left( {\frac{b}{{2a}}} \right)^2}\) ; Complete the square

    \({\left( {x + \frac{b}{{2a}}} \right)^2} = \frac{{{b^2}}}{{4{a^2}}} - \frac{c}{a}\)

    \({\left( {x + \frac{b}{{2a}}} \right)^2} = \frac{{{b^2} - 4ac}}{{4{a^2}}}\)

    \(x + \frac{b}{{2a}} = \frac{{\sqrt {{b^2} - 4ac} }}{{\sqrt {4{a^2}} }}\)

    \(x = \frac{{ - b}}{{2a}} + \frac{{\sqrt {{b^2} - 4ac} }}{{2a}}\)

    \(x = \frac{{ - b \pm \sqrt {{b^2} - 4ac} }}{{2a}}\)