Question

Solve for X:x^2+5x-(a^2+a-6)

Answer 1

Given:x²+5x-(a²+a-6)=0

To find:The roots of the given equation

•For this type of equations,the constant term need to be simplified.

Constant term:

a²+a-6

→a²+3a-2a-6

→a(a+3)-2(a+3)

→(a+3)(a-2)

Splitting 5x in accordance with a+3 and a-2

5x=[(a+3)-(a-2)]x

Now,

x²+5x-(a²+a-6)=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-2)][x+(a+3)]=0

→x= a-2 or -(a+3)

The roots are a-2 and -(a+3)