Solve the equation by using the formula $x^{2} - 8 x + 1 = 0$

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Solution

Compare the equation with standard form
$x = \frac{- b \pm \sqrt{b^{2} - 4 a c}}{2 a}$
$= \frac{- (- 8) \pm \sqrt{{(- 8)}^{2} - 4 \times 1 \times 1}}{2 \times 1}$
$= \frac{8 \pm \sqrt{64 - 4}}{2} = \frac{8 \pm \sqrt{60}}{2}$
$= \frac{8 \pm \sqrt{4 \times 15}}{2} = \frac{8 \pm 2 \sqrt{15}}{2}$
$= 4 \pm \sqrt{15}$

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