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We want to find the values of \(x\) satisfying \(ax^2 + bx + c = 0\). This is equivalent to

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

“Completing the square” yields

\[(x+\frac{b}{2a})^2 - \frac{b^2}{4a^2} + \frac{c}{a} = 0.\]

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