Question

Solve for x: x^2+5x-(a^2+a-6)=0

Answer 1

Answer:

- ( a + 3 ) , ( a - 2 )

Step-by-step explanation:

x^2 + 5x - ( a^2 + a - 6 ) = 0

STEP/TIP:--Always factorise the constant term

x^2 + 5x - ( a^2 - 2a + 3a - 6 )

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

x^2 + 5x - ( a - 2 )( a + 3 )

STEP/TIP:--Try looking for a breaking of coefficient of x just like the factorised constant term ( toughest part )

TIP(for sign confusion and breaking) :--

Always check the coefficient of x in question which is 5 in this case.

Use the constants of factorised constant to make it which is

2 and 3 into 5

Here, clearly ( 2 + 3 ) = 5

x^2 + ( a + 3 )x - ( a - 2 )x - ( a - 2 )( a + 3 )

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

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

[x + a + 3][x - a + 2]

So, x = -( a + 3 ) or x = (a - 2)

Hope it helps.....