Solve the equation. Identify any extraneous solutions.

6 is a solution, -4 is extraneous

Step-by-step 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

f is the midpoint of

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