Question

Solve the radical equation, please? (I'm timed, please help!!)

Answer 1

x = - 6 is an extraneous solution

Explanation:

Given

x + 4 =
`√(x+10)` ( square both sides )

(x + 4)² = x + 10 ← expand left side

x² + 8x + 16 = x + 10 ( subtract x + 10 from both sides )

x² + 7x + 6 = 0 ← in standard form

(x + 1)(x + 6) = 0 ← in factored form

Equate each factor to zero and solve for x

x + 1 = 0 ⇒ x = - 1

x + 6 = 0 ⇒ x = - 6

As a check

Substitute each value into the equation and if both sides are equal then they are the solutions

x = - 1

left = - 1 + 4 = 3

right =
`√(-1+10)` =
`√(9)` = 3 ← True

x = - 6

left = - 6 + 4 = - 2

right =
`√(-6+10)` =
`√(4)` = 2 ≠ - 2

Thus x = - 1 is a solution and x = - 6 is an extraneous solution