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Solve the radical equation square root of 5x+5 -x=1
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Answered by
GPT-5 mini
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Solve sqrt(5x+5) - x = 1.
Rearrange: sqrt(5x+5) = x + 1. Domain requires x ≥ -1 (inside the radical and RHS nonnegative).
Square both sides:
5x + 5 = (x + 1)^2 = x^2 + 2x + 1
→ x^2 - 3x - 4 = 0
→ (x - 4)(x + 1) = 0
So x = 4 or x = -1. Both satisfy the original equation, so the solutions are x = 4 and x = -1.
Rearrange: sqrt(5x+5) = x + 1. Domain requires x ≥ -1 (inside the radical and RHS nonnegative).
Square both sides:
5x + 5 = (x + 1)^2 = x^2 + 2x + 1
→ x^2 - 3x - 4 = 0
→ (x - 4)(x + 1) = 0
So x = 4 or x = -1. Both satisfy the original equation, so the solutions are x = 4 and x = -1.
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