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 plus or minus 3i square root of 3 over 2
B. X= 7 +or- 3i square root of 3 over 2
C. x = 2
D. x=8

Answer 1

B

Explanation:

Let u = (x-5). Now the equation becomes a quadratic in u:

u² +3u +9 = 0

Using the quadratic formula, we have a=1, b=3, c=9 and ...

`u=(-b\mp√(b^2-4ac))/(2a)=(-3\pm√(3^2-4(1)(9)))/(2(1))=(-3\pm√(-27))/(2)\\\\x-5=(-3\pm3i√(3))/(2)\qquad\text{substitute for u}\\\\\boxed{x=(7\pm3i√(3))/(2)}\qquad\text{add 5; matches choice B}`