Q:

What are the solutions of the equation (x – 3)^2 + 2(x – 3) – 8 = 0? Use u substitution to solve.x = –5 and x = 1x = –1 and x = 5x = –1 and x = –7x = 1 and x = 7

Accepted Solution

A:
Answer:x = -1 and x = 5Step-by-step explanation:What are the solutions of the equation (x – 3)² + 2(x – 3) -8 = 0? Use u substitution to solve.(x – 3)² + 2(x – 3) -8 = 0   -------------------------------------------------------(1)To solve this problem, we will follow the steps below;let u = x-3we will replace x-3 by u in the given equation:(x – 3)² + 2(x – 3) -8 = 0  u² + 2u -8 = 0  ----------------------------------------------------------- --------------(2)We will now solve the above quadratic equationfind two numbers such that its product gives -8 and its sum gives 2The two numbers are 4 and -2That is; 4×-2 = -8    and 4+(-2) = 2we will replace 2u by (4u -2u)  in equation (2)u² + 2u -8 = 0u² + 4u - 2u -8 = 0u(u+4) -2(u+4) = 0(u+4)(u-2) = 0Either  u + 4 = 0             u = -4or u-2 = 0u = 2Either u = -4    or u = 2But  u = x-3x = u +3when u = -4x = u + 3x = -4 + 3x=-1when u = 2x = u + 3x = 2 + 3x=5Therefore, x = -1  and  x =5x