Question

X2 + 4x - 32 = 0. Solve equation

Answer 1

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

Answer 2

Answer:2x + 4x -32 = 0

6x -32 = 0

6x =32

x = 32/6