Question

Solve the radical equation. x + 4 = square root of x plus 10. What is the extraneous solution to the radical equation?

Answer 1

C The solution -6 is extraneous

Explanation:

got it right on edge

Answer 2

see explanation

Explanation:

given

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

(x + 4)² = x + 10

x² + 8x + 16 = x + 10

rearrange into standard form : ax² + bx + c = 0

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 these values into the equation and if the left side equals the right side then they are solutions

x = - 1 : left = - 1 + 4 = 3 , right =
`√(-1+10)` =
`√(9)` = 3

Hence x = - 1 is a solution

x = - 6 : left = - 6 + 4 = - 2 , right =
`√(-6+10)` =
`√(4)` = 2

Hence x = - 6 is an extraneous solution