Question

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

Answer 1

x = 6

Explanation:

Given

x - 2 =
`√(x+10)`

Square both sides to clear the radical

(x - 2)² = x + 10 ← expand left side using FOIL

x² - 4x + 4 = x + 10 ( subtract x + 10 from both sides )

x² - 5x - 6 = 0 ← in standard form

(x - 6)(x + 1) = 0 ← in factored form

Equate each factor to zero and solve for x

x - 6 = 0 ⇒ x = 6

x + 1 = 0 ⇒ x = - 1

As a check

Substitute these values into the equation and if both sides are equal then they are the solutions.

x = - 1 : left side = - 1 - 2 = - 3

right side =
`√(-1+10)` =
`√(9)` = 3 ≠ - 3

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x = 6 : left side = 6 - 2 = 4

right side =
`√(6+10)` =
`√(16)` = 4

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Thus x = 6 is the solution, x = - 1 is an extraneous solution