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Quadratic Formula

Solve x2 - ...

Question

Solve $x^{2} - 4 x + (a^{2} - b^{2}) = 0$

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Solution

$x^{2} - 4 x + a^{2} - b^{2} = 0$

$x_{1, 2} = \frac{- b \pm \sqrt{b^{2} - 4 a c}}{2 a}$

$x = \frac{- (- 4) \pm \sqrt{{(- 4)}^{2} - 4 \cdot 1 (a^{2} - b^{2})}}{2 \cdot 1}$

$= \frac{4 + \sqrt{{(- 4)}^{2} - 4 \cdot 1 \cdot (a^{2} - b^{2})}}{2 \cdot 1}$

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

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