quadradtic equasion

Question

Solve the following quadraric equasion by factoring

 

x(small 2)-6x-27=0

Answer 1

X² - 6x -27 =0

( X -9) ( X+3) =0

 

 X =9   X =-3

Answer 2

The problem is x² - 6x -27 = 0

The factors of this can be expressed as (x + a)*(x + b) = 0

There are two values of x because this is a quadratic equation. If the factors are expanded, we get the following:

   x² + (a + b)x + a*b = 0.

Applying this into the problem, we get a + b = -6, and a*b = -27. 

27 has the following factors: 1,3 and 9. Based on this information, a must be -9 and b must be 3. Note that BOTH conditions (a + b and a*b) must be satisfied.

The factors of the problem are then (x - 9) * (x + 3) = 0.

x can be either 9 or -3, by equating each bracket individually to 0. ( x - 9 = 0, and x + 3 = 0). Hope that helped.