Answer:
x = 4 or x = -8
Step-by-step explanation:
x² + 4x - 32 = 0
we see that the discriminant (i.e b²-4ac) is positive and non-zero, this means that we expect 2 distinct real solutions for x.
solving by factorization:
i.e, the above quadratic equation can be factorized as
(x + A) (x+B) = 0,
where,
A·B = -32 (i.e constant term) and A+B = 4 (i.e x-coefficient)
By inspection of the x-coefficient and the constant term, we can see that the constant term factorizes as -32 = -4 x 8.
We also see that these 2 factors of -32 add up to equal the x-coefficient
hence we can conclude that A and B are -4 and 8.
Therefore, the equation above becomes:
(x + A) (x+B) = 0
(x -4 ) (x+8) = 0
(x-4) = 0 or (x+8) = 0
x = 4 or x = -8
