Question

`x = √(2x + 24)`
Solve the equation. Identify any extraneous solutions.​

Answer 1

6 is a solution, -4 is extraneous

Explanation:

x = sqrt(2x+24)

square each side

x^2 =( sqrt(2x+24))^2

x^2 = 2x+24

Subtract 2x from each side

x^2 -2x = 2x-2x+24

x^2 -2x =24

Subtract 24 from each side

x^2 -2x-24 = 24-24

x^2 -2x-24 =0

Factor

(x-6) (x+4) =0

Using the zero product property

x=6 x=-4

Check the solutions in the original equation

x=6

6 = sqrt(2*6+24)

6 = sqrt(12+24)

6 = sqrt(36)

6=6

x=-4

-4 = sqrt(2*-4+24)

-4 = sqrt(-8+24)

-4 = sqrt(16)

-4=4 not a solution