二次方程式の解の公式の証明

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a x^{2} + b x + c = 0

x^{2} + \frac{b}{a} x + \frac{c}{a} = 0

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

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

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

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

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

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

x + \frac{b}{2 a} = \pm \sqrt{\frac{b^{2} - 4 a c}{4 a^{2}}}

x + \frac{b}{2 a} = \pm \frac{\sqrt{b^{2} - 4 a c}}{2 a}

x = - \frac{b}{2 a} \pm \frac{\sqrt{b^{2} - 4 a c}}{2 a}

x = \frac{- b \pm \sqrt{b^{2} - 4 a c}}{2 a}