Solve the quadratic equation: $(x + 8)^{2} - 5 = 31$

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Solution

The given quadratic equation $(x + 8)^{2} - 5 = 31$ can be simplified as follows:

$(x + 8)^{2} - 5 = 31 \Rightarrow (x + 8)^{2} = 31 + 5 \Rightarrow (x + 8)^{2} = 36 \Rightarrow (x + 8) = \pm \sqrt{36} \Rightarrow (x + 8) = \pm 6 \Rightarrow x + 8 = - 6, x + 8 = 6 \Rightarrow x = - 6 - 8, x = 6 - 8 \Rightarrow x = - 14, x = - 2$

Hence, $x = - 2, - 14$ .

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\frac{x - 1}{x - 2} + \frac{x - 3}{x - 4} = 3 \frac{1}{3}

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Solve the following quadratic equation by factorization.
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