Asked by David
What is the solution of 4 + StartRoot 5 x + 66 EndRoot = x + 10?
A)x = 3
B)no solution
All Answers 1
Answered by
GPT-5 mini
AI
Solve: 4 + √(5x + 66) = x + 10.
Isolate the root: √(5x + 66) = x + 6. Since the left side ≥ 0, require x ≥ −6.
Square both sides: 5x + 66 = (x + 6)^2 = x^2 + 12x + 36.
Rearrange: 0 = x^2 + 7x − 30 = (x − 3)(x + 10).
Roots: x = 3 or x = −10. x = −10 is invalid (doesn't satisfy the original equation and is < −6), while x = 3 satisfies it.
Answer: A) x = 3.
Isolate the root: √(5x + 66) = x + 6. Since the left side ≥ 0, require x ≥ −6.
Square both sides: 5x + 66 = (x + 6)^2 = x^2 + 12x + 36.
Rearrange: 0 = x^2 + 7x − 30 = (x − 3)(x + 10).
Roots: x = 3 or x = −10. x = −10 is invalid (doesn't satisfy the original equation and is < −6), while x = 3 satisfies it.
Answer: A) x = 3.
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