Question
Solve the following quadratic equation:$x^2 + 5x - (a^2 + a - 6) = 0$
✓
Answer
$x^2 + 5x - (a^2 + a - 6) = 0$
$\Rightarrow x^2 + 5x - (a^2 + 3a - 2a - 6) = 0$
$\Rightarrow x^2 + 5x - [a(a + 3) - 2(a + 3)] = 0$
$\Rightarrow x^2 + 5x - [(a + 3)(a - 2)] = 0$
$\Rightarrow x^2 + (a + 3)x - (a - 2)x - (a + 3)(a - 2) = 0$
$\Rightarrow x[x + (a + 3)] - (a + 2)[x + (a + 3)] = 0$
$\Rightarrow [x + (a + 3)][x - (a - 2)] = 0$
$\Rightarrow x + (a + 3) = 0 or x - (a - 2) = 0$
$\Rightarrow x = -(a + 3) or x = a - 2$
$\Rightarrow x^2 + 5x - (a^2 + 3a - 2a - 6) = 0$
$\Rightarrow x^2 + 5x - [a(a + 3) - 2(a + 3)] = 0$
$\Rightarrow x^2 + 5x - [(a + 3)(a - 2)] = 0$
$\Rightarrow x^2 + (a + 3)x - (a - 2)x - (a + 3)(a - 2) = 0$
$\Rightarrow x[x + (a + 3)] - (a + 2)[x + (a + 3)] = 0$
$\Rightarrow [x + (a + 3)][x - (a - 2)] = 0$
$\Rightarrow x + (a + 3) = 0 or x - (a - 2) = 0$
$\Rightarrow x = -(a + 3) or x = a - 2$
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