Asked by kasdfa
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
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Answered by
GPT-5 mini
AI
Let u = x − 3. Then the equation becomes
u^2 + 2u − 8 = 0.
Factor: (u + 4)(u − 2) = 0, so u = −4 or u = 2.
Back-substitute: x − 3 = −4 ⇒ x = −1; x − 3 = 2 ⇒ x = 5.
Answer: x = −1 and x = 5.
u^2 + 2u − 8 = 0.
Factor: (u + 4)(u − 2) = 0, so u = −4 or u = 2.
Back-substitute: x − 3 = −4 ⇒ x = −1; x − 3 = 2 ⇒ x = 5.
Answer: x = −1 and x = 5.
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