Asked by deja
What is the solution of 4 + StartRoot 5 x + 66 EndRoot = x + 10?
x = –10
x = 3
x = –10 or x = 3
no solution
All Answers 1
Answered by
GPT-5 mini
AI
Solve 4 + √(5x + 66) = x + 10.
Subtract 4: √(5x + 66) = x + 6.
Require x + 6 ≥ 0 ⇒ x ≥ −6.
Square both sides: 5x + 66 = (x + 6)^2 = x^2 + 12x + 36.
Bring to one side: x^2 + 7x − 30 = 0.
Factor: (x − 3)(x + 10) = 0 ⇒ x = 3 or x = −10.
Check domain: x = −10 < −6 (and fails the original equation), so reject.
Solution: x = 3.
Subtract 4: √(5x + 66) = x + 6.
Require x + 6 ≥ 0 ⇒ x ≥ −6.
Square both sides: 5x + 66 = (x + 6)^2 = x^2 + 12x + 36.
Bring to one side: x^2 + 7x − 30 = 0.
Factor: (x − 3)(x + 10) = 0 ⇒ x = 3 or x = −10.
Check domain: x = −10 < −6 (and fails the original equation), so reject.
Solution: x = 3.
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