Find one value of x that is a solution to the equation:
(x^2+4)^2 – 11(x^2+4) + 24 = 0

x = ±2

 x = ±i

Step-by-step explanation:

(x^2+4)^2 – 11(x^2+4) + 24 = 0

Let m = x^2 +4

(m)^2 – 11(m) + 24 = 0

Solving this quadratic

What two numbers multiply to 24 and add to -11

-8*-3 =24

-8-3 = -11

(m-8)(m-3) =0

m = 8   m=3

Now substitute back

x^2 +4 = 8    x^2 +4 = 3

x^2 +4-4 = 8-4    x^2+4-4 = 3-4

x^2 = 4                      x^2 = -1

Taking the square root

sqrt(x^2) = sqrt(4)                      sqrt(x^2) = sqrt(-1)

x = ±2                                           x = ±i