Question

Solve for x :x² + 5x - (a²+a-6) = 0​

Answer 1

⇒x2+5x-(a2+a-6)=0

⇒x2+5x−(a+3)(a−2)=0

⇒x2+[(a+3)−(a−2)]x−(a+3)(a−2)=0

⇒x2+(a+3)x−(a−2)x−(a+3)(a−2)=0

⇒x[x+(a+3)]−(a−2)[x+(a+3)]=0

⇒[x+(a+3)][x−(a−2)]=0

⇒[x+(a+3)]=0 or [x−(a−2)]=0

⇒x=−(a+3) or x=(a−2)

Answer 2

Step-by-step explanation:

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$equation \: = {x}^{2} + 5x - ( {a}^{2} + a - 6 )\\ {x}^{2} + 5x - (a + 3)(a - 2) \\ \\ {x}^{2} + (a + 3)x - (a - 2)x - (a + 3)( - 2) \\ \\ x(x + a + 3) \: - (a - 2)(x + a + 3) \\ \\ (x + a + 3)(x - a + 2) \\ \\ x = - (a + 3) \: \: or \\ x = (a - 2)$