Question

What is the solution of the equation (x - 5)2 + 3(x - 5) + 9 =0? Use u substitution and the quadratic formula to solve.

-323115
o *-73in3
O.x=2
X-8

Answer 1

x = 7/2 ± 3/2*(i√3)

Explanation:

The equation is

(x - 5)^2 + 3(x - 5) + 9 =0

Let A = (x-5)

The equation becomes now

(A)^2 + 3(A) + 9 =0

We then apply the quadratic formula

A = [-(3) ± √((3)^2-4(1)(9)) ]/ (2(1))

A = -3/2 ± 3/2*(i√3)

Now, we revert the substitution

(x-5) = -3/2 ± 3/2*(i√3)

x = 7/2 ± 3/2*(i√3)