Solve each of the following quadratic equations:
$x^{2} + 6 x - (a^{2} + 2 a - 8) = 0$

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Solution

$x^{2} + 6 x - (a^{2} + 2 a - 8) = 0$
Solving the Q.E in x,we have
$x = \frac{- b \pm \sqrt{b^{2} - 4 a c}}{2 a} = \frac{- 6 \pm \sqrt{6^{2} - 4 (- (a^{2} + 2 a - 8))}}{2} = \frac{- 6 \pm \sqrt{36 + 4 a^{2} + 8 a - 32}}{2} = \frac{- 6 \pm \sqrt{4 a^{2} + 8 a + 4}}{2} = \frac{- 6 \pm \sqrt{4 (a + 1)^{2}}}{2}$
$x = \frac{- 6 \pm 2 (a + 1)}{2} = - 3 + a + 1 o r - 3 - a - 1 = a - 2 o r - a - 4$

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