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

x = -5 and x = 1
x = -1 and x = 5
x= -1 and x = -7
x = 1 and x = 7

2 Answers

1 vote

Answer:

x=-1 and x=5

Explanation:

User Wmute
by
8.4k points
2 votes

Answer:

x = -1 and x = 5

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

User Ccnokes
by
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