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

x = 6

Step-by-step explanation:

Given

x - 2 =

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 = = = 3 ≠ - 3

---------------------------------------------------

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

right side = = = 4

----------------------------------------------

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