Question

What are the solutions of the equation (x – 3)2 + 2(x – 3) -8 = 0? Use u substitution to solve.

Answer 1

Answer:

x = -1 and x = 5

Step-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-3

we 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 equation

find two numbers such that its product gives -8 and its sum gives 2

The two numbers are 4 and -2

That is; 4×-2 = -8    and 4+(-2) = 2

we will replace 2u by (4u -2u)  in equation (2)

u² + 2u -8 = 0

u² + 4u - 2u -8 = 0

u(u+4) -2(u+4) = 0

(u+4)(u-2) = 0

Either  u + 4 = 0

            u = -4

or

u-2 = 0

u = 2

Either u = -4    or u = 2

But  u = x-3

x = u +3

when u = -4

x = u + 3

x = -4 + 3

x=-1

when u = 2

x = u + 3

x = 2 + 3

x=5

Therefore, x = -1  and  x =5

x