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.

A) x=-3+3i√3/2 B) x=7+3i√3/2 C) x=2 D) x=8

Answer 1

x = 7+/-3i sqrt3 over 2

Explanation:

Answer 2

`x = (7 \pm 3i√(3))/(2)`

Explanation:

(x – 5)^2 + 3(x – 5) + 9 = 0

This is a quadratic equation in x - 5.

Let u = x - 5, then the quadratic equation becomes:

u^2 + 3u + 9 = 0

We can use the quadratic formula to solve for u.

`u = (-b \pm √(b^2 - 4ac))/(2a)`

`u = (-3 \pm √(3^2 - 4(1)(9)))/(2(1))`

`u = (-3 \pm √(9 - 36))/(2)`

`u = (-3 \pm √(-27))/(2)`

`u = (-3 \pm 3i√(3))/(2)`

Since u = x - 5, now we substitute x - 5 for u and solve for x.

`x - 5 = (-3 \pm 3i√(3))/(2)`

`x = (-3 \pm 3i√(3))/(2) + 5`

`x = (-3 \pm 3i√(3))/(2) + (10)/(2)`

`x = (7 \pm 3i√(3))/(2)`