Question

Select the correct answer.
What is the solution to the equation?

Answer 1

B

Explanation:

`√(x)` + 6 = x ( subtract 6 from both sides )

`√(x)` = x - 6 ( square both sides )

x = (x - 6)² ← expand using FOIL

x = x² - 12x + 36 ( subtract x from both sides )

0 = x² - 13x + 36 , that is

x² - 13x + 36 = 0 ← in standard form

(x - 4)(x - 9) = 0 ← in factored form

Equate each factor to zero and solve for x

x - 4 = 0 ⇒ x = 4

x - 9 = 0 ⇒ x = 9

As a check

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

x = 4

left side =
`√(4)` + 6 = 2 + 6 = 8

right side = x = 4

Since 8 ≠ 4 then x = 4 is an extraneous solution

x = 9

left side =
`√(9)` + 6 = 3 + 6 = 9

right side = x = 9

Thus the solution is x = 9 → B