Question

Explain the steps used to solve x - 2 = v(x + 10) and check for extraneous solutions.

Answer 1

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Question
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x - 2 = √(x + 10) 

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Square both sides
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(x - 2)² = (√(x + 10))²
(x - 2)² = (x + 10)   ← square and square root would will net off each other

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Remove brackets
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x² - 4x + 2² = x + 10
x² - 4x + 4 = x + 10

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minus x + 10 on both sides
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x² - 4x + 4 - x - 10 = 0
x² - 5x - 6 = 0

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Factorise the left side
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(x - 6)(x + 1) = 0

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Apply zero product property 
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x -6 = 0  or  x +1 = 0

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Solve x
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x = 6 or x = -1

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Answer: x = 6 or x = -1
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